strong convergence theorem for nonexpansive mappings on star shaped sets in hilbert spaces abstract in this paper using the concept of attractive points of a nonlinear mapping we obtain a strong convergence theorem of halpern s type 7 for nonexpansive mappings in a star shaped subset of a hilbert space using this result we obtain a new fixed point theorem and a strong convergence theorem which generalizes wittmann s theorem 26

hybrid iterative scheme for fixed point problem infinite systems of equilibrium and variational inequality problems the purpose of this paper is to construct a new iterative scheme by the hybrid method and prove a strong convergence theorem for the approximation of a common fixed point of two countable families of weak relatively nonexpansive mappings which is also a common solution to infinite systems of equilibrium and variational inequality problems in a uniformly smooth and strictly convex real banach space with kadec klee property using the properties of a generalized f projection operator using this result we give some applications our results extend many known recent results in the literature

convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense abstract in this paper we prove a strong convergence of ishikawa scheme to a uniformly l lipschitzian and asymptotically pseudocontractive mappings in the intermediate sense no compactness assumption is imposed either on t or c and computation of intersection of closed convex sets c n and q n for each n 1 is not required we also obtain convergence results in this direction for asymptotically strict pseudocontractive mappings in the intermediate sense our theorems improve and unify most of the results that have been proved for this important class of nonlinear mappings

convergence of ishikawa s iteration method for pseudocontractive mappings let c be a nonempty closed and convex subset of a real hilbert space h let ti c c i 1 2 n be a finite family of lipschitz pseudocontractive mappings it is our purpose in this paper to prove strong convergence of ishikawa s method to a common fixed point of a finite family of lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty no compactness assumption is imposed either on t or on c moreover computation of the closed convex set cn for each n 1 is not required the results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings

shrinking projection methods for firmly nonexpansive mappings abstract the purpose of this paper is to study the shrinking projection method for firmly nonexpansive mappings the method gives us a strong convergence iteration for a family of firmly nonexpansive mappings and also permit us to obtain a sufficient condition for the existence of a fixed point of a firmly nonexpansive mapping

control of stochastic discrete event systems modeled by probabilistic languages in garg et al 1999 and garg 1992 the formalism of probabilistic languages for modeling the stochastic qualitative behavior of discrete event systems dess was introduced in this paper we study their supervisory control where the control is exercised by dynamically disabling certain controllable events thereby nulling the occurrence probabilities of disabled events and increasing the occurrence probabilities of enabled events proportionately this is a special case of probabilistic supervision introduced in lawford and wonham 1993 the control objective is to design a supervisor such that the controlled system never executes any illegal traces their occurrence probability is zero and legal traces occur with minimum prespecified occurrence probabilities in other words the probabilistic language of the controlled system lies within a prespecified range where the upper bound is a nonprobabilistic language representing a legality constraint we provide a condition for the existence of a supervisor we also present an algorithm to test this existence condition when the probabilistic languages are regular so that they admit probabilistic automata representation with finitely many states next we give a technique to compute a maximally permissive supervisor online

strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces the purpose of the paper is to introduce modified halpern and ishikawa iteration for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in banach spaces we also consider two strong convergence theorems for relatively nonexpansive mappings with some proper restriction

approximate generalized proximal type method for convex vector optimization problem in banach spaces in this paper we consider a convex vector optimization problem of finding weak pareto optimal solutions for an extended vector valued map from a uniformly convex and uniformly smooth banach space to a real banach space with respect to the partial order induced by a closed convex and pointed cone with a nonempty interior we propose an inexact vector valued proximal type point algorithm based on a lyapunov functional when the iterates are computed approximately and prove the sequence generated by the algorithm weakly converges to a weak pareto optimal solution of the vector optimization problem under some mild conditions our results improve and generalize some known results

convergence of the modified mann s iteration method for asymptotically strict pseudo contractions abstract let c be a closed convex subset of a real hilbert space h and assume that t is an asymptotically strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the modified mann s algorithm generates a sequence x n via the formula x n 1 n x n 1 n t n x n n 0 it is proved that if the control sequence n is chosen so that n 1 for some 0 1 then x n converges weakly to a fixed point of t we also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence

recursive markov chains stochastic grammars and monotone systems of nonlinear equations we define recursive markov chains rmcs a class of finitely presented denumerable markov chains and we study algorithms for their analysis informally an rmc consists of a collection of finite state markov chains with the ability to invoke each other in a potentially recursive manner rmcs offer a natural abstract model for probabilistic programs with procedures they generalize in a precise sense a number of well studied stochastic models including stochastic context free grammars scfg and multi type branching processes mt bp we focus on algorithms for reachability and termination analysis for rmcs what is the probability that an rmc started from a given state reaches another target state or that it terminatesq these probabilities are in general irrational and they arise as least fixed point solutions to certain monotone systems of nonlinear equations associated with rmcs we address both the qualitative problem of determining whether the probabilities are 0 1 or in between and the quantitative problems of comparing the probabilities with a given bound or approximating them to desired precision we show that all these problems can be solved in pspace using a decision procedure for the existential theory of reals we provide a more practical algorithm based on a decomposed version of multi variate newton s method and prove that it always converges monotonically to the desired probabilities we show this method applies more generally to any monotone polynomial system we obtain polynomial time algorithms for various special subclasses of rmcs among these for scfgs and mt bps equivalently for 1 exit rmcs the qualitative problem can be solved in p time for linearly recursive rmcs the probabilities are rational and can be computed exactly in p time we show that our pspace upper bounds cannot be substantially improved without a breakthrough on long standing open problems the square root sum problem and an arithmetic circuit decision problem that captures p time on the unit cost rational arithmetic ram model we show that these problems reduce to the qualitative problem and to the approximation problem to within any nontrivial error for termination probabilities of general rmcs and to the quantitative decision problem for termination extinction of scfgs mt bps

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

supervisory control of a class of discrete event processes this paper studies the control of a class of discrete event processes i e processes that are discrete asynchronous and possibly nondeter ministic the controlled process is described as the generator of a formal language while the controller or supervisor is constructed from the grammar of a specified target language that incorporates the desired closed loop system behavior the existence problem for a supervisor is reduced to finding the largest controllable language contained in a given legal language two examples are provided

halpern s iteration for bregman strongly nonexpansive mappings in reflexive banach spaces we investigate strong convergence for bregman strongly nonexpansive mappings by halpern s iteration in the framework of reflexive banach spaces using the obtained result convergence for a family of bregman strongly nonexpansive mappings is also discussed as applications we apply our main result to problems of finding zeros of maximal monotone operators and equilibrium problems in reflexive banach spaces

approximating common fixed points of nonexpansive mappings and nonspreading mappings in a hilbert space abstract in this paper we obtain some fundamental properties for nonspreading mappings in a hilbert space further we study the approximation of common fixed points of nonexpansive mappings and nonspreading mappings in a hilbert space

hybrid approximation of solutions of nonlinear operator equations and application to equation of hammerstein type in this paper we study hybrid iterative scheme for finding a common element of set of solutions of generalized mixed equilibrium problem set of common fixed points of finite family of weak relatively nonexpansive mapping and null spaces of finite family of inverse strongly monotone mappings in a 2 uniformly convex and uniformly smooth real banach space our results extend improve and generalize the results of several authors which are announced recently application of our theorem to solution of equations of hammerstein type is of independent interest

metrics for labelled markov processes the notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions thus a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent this instability is due to the quantitative nature of probabilistic processes in a situation where the process behavior has a quantitative aspect there should be a more robust approach to process equivalence this paper studies a metric between labelled markov processes this metric has the property that processes are at zero distance if and only if they are bisimilar the metric is inspired by earlier work on logics for characterizing bisimulation and is related in spirit to the hutchinson metric

bisimulation for probabilistic transition systems a coalgebraic approach the notion of bisimulation as proposed by larsen and skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of aczel and mendier in terms of a set functor this coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving borel probability measures under reasonable conditions generalized probabilistic bisimilarity can be characterized categorically application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation

convergence of mann s type iteration method for generalized asymptotically nonexpansive mappings let c be a nonempty closed and convex subset of a real hilbert space h let t i c h i 1 2 n be a finite family of generalized asymptotically nonexpansive mappings it is our purpose in this paper to prove strong convergence of mann s type method to a common fixed point of t i i 1 2 n provided that the interior of common fixed points is nonempty no compactness assumption is imposed either on t or on c as a consequence it is proved that mann s method converges for a fixed point of nonexpansive mapping provided that interior of f t 0 the results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings

discrete time controlled markov processes with average cost criterion a survey this work is a survey of the average cost control problem for discrete time markov processes the authors have attempted to put together a comprehensive account of the considerable research on this problem over the past three decades the exposition ranges from finite to borel state and action spaces and includes a variety of methodologies to find and characterize optimal policies the authors have included a brief historical perspective of the research efforts in this area and have compiled a substantial yet not exhaustive bibliography the authors have also identified several important questions that are still open to investigation

weak and strong convergence theorems for nonspreading mappings in hilbert spaces abstract in this paper we first obtain a weak mean convergence theorem of baillon s type for nonspreading mappings in a hilbert space further using an idea of mean convergence we prove a strong convergence theorem for nonspreading mappings in a hilbert space

probabilistic supervisory control of probabilistic discrete event systems this paper considers supervisory control of probabilistic discrete event systems pdess pdess are modeled as generators of probabilistic languages the supervisory control problem considered is to find if possible a supervisor under whose control the behavior of a plant is identical to a given probabilistic specification the probabilistic supervisors we employ are a generalization of the deterministic ones previously employed in the literature at any state the supervisor enables disables events with certain probabilities necessary and sufficient conditions for the existence of such a supervisor and an algorithm for its computation are presented

a new algorithm for two finite families of demicontractive mappings and equilibrium problems in this paper we introduce a new algorithm for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of two finite families of demicontractive mappings the strong convergence theorem of the proposed algorithm is established under some suitable control conditions in a real hilbert space our result generalizes several recent results in the current literature

an analytical study of sound transmission through unbounded panels of functionally gradedmaterials the problem of sound transmission and reflection from unbounded panels of functionally graded materials is studied using an analytical approach by means of matrix manipulation and fourier component analysis the three dimensional 3 d governing equations of elastodynamics are converted into a system of ordinary differential equations with variable coefficients in the frequency and wavenumber domain integration of the ordinary differential equation system across the panel thickness leads to a closed form solution for the transfer matrix analytical expressions are then obtained for sound reflection and transmission coefficients for panels of functionally graded materials the present model is used to predict sound transmission losses for various panel examples the results compare well with published data from other methods thereby validating the accuracy of the formulation developed in this study

halpern type iterations for strongly relatively nonexpansive mappings in banach spaces in this paper we note that the main convergence theorem in zhang et al 2011 21 is incorrect and we prove a correction we also modify halpern s iteration for finding a fixed point of a strongly relatively nonexpansive mapping in a banach space consequently two strong convergence theorems for a relatively nonexpansive mapping and for a mapping of firmly nonexpansive type are deduced using the concept of duality theorems we obtain analogue results for strongly generalized nonexpansive mappings and for mappings of firmly generalized nonexpansive type in addition we study two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a banach space

on hybrid projection methods for asymptotically quasi φ nonexpansive mappings the purpose of this paper is to consider the problem of approximating a common fixed point of two asymptotically quasi f nonexpansive mappings based on hybrid projection methods strong convergence theorems are established in a real banach space

strong convergence theorems for two countable families of weak relatively nonexpansive mappings and applications abstract the purpose of this article is to prove strong convergence theorems for common fixed points of two countable families of weak relatively nonexpansive mappings in banach spaces in order to get the strong convergence theorems the monotone hybrid algorithms are presented and are used to approximate the common fixed points using this result we also discuss the problem of strong convergence concerning the maximal monotone operators in a banach space the results of this article modify and improve the results of matsushita and takahashi s matsushita w takahashi a strong convergence theorem for relatively nonexpansive mappings in a banach space j approx theory 134 2005 257 266 and the results of plubtieng and ungchittrakool s plubtieng k ungchittrakool strong convergence theorems for a common fixed point of two relatively nonexpansive mappings in a banach space j approx theory 149 2007 103 115 and the results of su et al y su z wang and h xu strong convergence theorems for a common fixed point of two hemi relatively nonexpansive mappings nonlinear anal 71 2009 5616 5628 and many others

equivalent theorems of the convergence between proximal type algorithms abstract the main aim of this work is to give the equivalence of the convergence between proximal type algorithms our convergence analysis covers rockafellar type proximal point algorithm with a weak contraction for finding zeros of accretive operators as well as browder and halpern type iterations and viscosity approximation methods for finding fixed points of nonexpansive type mappings in banach spaces we also provide simple proofs of some results of wong sahu and yao n c wong d r sahu j c yao solving variational inequalities involving nonexpansive type mappings nonlinear anal 69 12 2008 4732 4753

finite termination of the proximal point algorithm in banach spaces abstract in this paper we show that the convex optimization problem can be solved by the proximal point algorithm in a finite number of steps under the assumption that the solution set is a set of weak sharp minima

modified block iterative algorithm for quasi ϕ asymptotically nonexpansive mappings and equilibrium problem in banach spaces abstract the purpose of this paper is to propose a modified block iterative algorithm for find a common element of the set of common fixed points of an infinite family of quasi asymptotically nonexpansive mappings and the set of an equilibrium problem under suitable conditions some strong convergence theorems are established in a uniformly smooth and strictly convex banach space with the kadec klee property as an application at the end of the paper a numerical example is given the results presented in the paper improve and extend the corresponding results in qin et al convergence theorems of common elements for equilibrium problems and fixed point problem in banach spaces j comput appl math 225 2009 20 30 zhou et al convergence theorems of a modified hybrid algorithm for a family of quasi asymptotically nonexpansive mappings j appl math compt 17 march 2009 doi 10 1007 s12190 009 0263 4 takahashi and zembayshi strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces nonlinear anal 70 2009 45 57 wattanawitoon and kumam strong convergence theorems by a new hybrid projection algorithm for fixed point problem and equilibrium problems of two relatively quasi nonexpansive mappings nonlinear anal hybrid syst 3 2009 11 20 and matsushita and takahashi a strong convergence theorem for relatively nonexpansive mappings in banach spaces j approx theory 134 2005 257 266 and others

a modified hybrid projection method for solving generalized mixed equilibrium problems and fixed point problems in banach spaces in this paper we introduce a modified new hybrid projection method for finding the set of solutions of the generalized mixed equilibrium problems and the convex feasibility problems for an infinite family of closed and uniformly quasi asymptotically nonexpansive mappings strong convergence theorems are established in a uniformly smooth and strictly convex banach space which also enjoys the kadec klee property our results improve and extend the corresponding results announced by qin et al 2010 and many authors

blackwell optimality in markov decision processes with partial observation a blackwell epsilon optimal strategy in a markov decision process is a strategy that is epsilon optimal for every discount factor sufficiently close to 1 we prove the existence of blackwell epsilon optimal strategies in finite markov decision processes with partial observation

exact solution for thermoelastic deformations of functionally graded thick rectangular plates an exact solution is obtained for three dimensional deformations of a simply supported functionally graded rectangular plate subjected to mechanical and thermal loads on its top and or bottom surfaces suitable temperature and displacement functions that identically satisfy boundary conditions at the edges are used to reduce the partial differential equations governing the thermomechanical deformations to a set of coupled ordinary differential equations in the thickness coordinate which are then solved by employing the power series method the exact solution is applicable to both thick and thin plates results are presented for two constituent metal ceramic functionally graded rectangular plates that have a power law through the thickness variation of the volume fractions of the constituents the effective material properties at a point are estimated by either the mori tanaka or the self consistentschemes exact displacementsand stressesatseveral locations for mechanical and thermal loads are used toassess theaccuracyof the classical plate theory thee rst ordershear deformation theory and athird order shear deformation theory for functionally graded plates results are alsocomputed for a functionally graded plate with material properties derived by the mori tanaka method the self consistent scheme and a combination of these two methods

approximating and computing behavioural distances in probabilistic transition systems in an earlier paper we presented a pseudometric on the states of a probabilistic transition system yielding a quantitative notion of behavioural equivalence the behavioural pseudometric was defined via the terminal coalgebra of a functor based on a metric on borel probability measures in the present paper we give a polynomial time algorithm based on linear programming to calculate the distances between states up to a prescribed degree of accuracy

convergence theorems for mixed equilibrium problems variational inequality problem and uniformly quasi ϕ asymptotically nonexpansive mappings abstract we introduce a modified block hybrid projection algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi asymptotically nonexpansive mappings the set of the variational inequality for an inverse strongly monotone operator the set of solutions of the mixed equilibrium problems then we obtain strong convergence theorems for the sequences generated by this process in a 2 uniformly convex and uniformly smooth banach space our results extend and improve ones from several earlier works

an iterative method for equilibrium problems and a finite family of relatively nonexpansive mappings in a banach space abstract in this paper we introduce a new iterative method for finding a common element of the set of fixed points of a finite family of relatively nonexpansive mappings and the set of solutions of an equilibrium problem in uniformly convex and uniformly smooth banach spaces then we prove a strong convergence theorem by using the generalized projection

strong and weak convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces abstract in this paper we introduce two iterative sequences for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a banach space then we study the strong and weak convergence of the sequences

convergence theorems of common elements for equilibrium problems and fixed point problems in banach spaces the purpose of this paper is to introduce hybrid projection algorithms for finding a common element of the set of common fixed points of two quasi f nonexpansive mappings and the set of solutions of an equilibrium problem in the framework of banach spaces our results improve and extend the corresponding results announced by many others

strongly convergent net given by a fixed point theorem for firmly nonexpansive type mappings abstract in this paper using a fixed point theorem which was recently obtained by the authors for firmly nonexpansive type mappings we prove a strong convergence theorem of browder s type in banach spaces using our result we study the approximation of zero points of monotone operators in banach spaces

strong convergence theorems for infinite family of relatively quasi nonexpansive mappings and systems of equilibrium problems abstract in this paper we construct a new iterative scheme by hybrid method for approximation of common element of set of common fixed points of countably infinite family of relatively quasi nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex and uniformly smooth real banach space using the properties of generalized f projection operator then we prove strong convergence of the scheme to a common element of the two sets furthermore we apply our results to solve convex minimization problem our results extend important recent results

iterative schemes for approximating solutions of generalized variational inequalities in banach spaces abstract in this paper we introduce two iterative schemes for approximating solutions of generalized variational inequalities in the setting of banach spaces the existence of solutions of this general problem and the convergence of the proposed iterative schemes to a solution are established

propagation properties of acoustic waves inside periodic pipelines abstract this paper presents a new method to model and to simulate the propagation properties of the acoustic wave in periodic pipelines first an ideal model of pipeline and its dispersion equations of acoustic waves are constructed and described in detail in order to implement this method subsequently the classical finite difference method is applied to determine the boundary conditions of the pipelines in addition the transfer matrix method is used to simulate the propagation process of the acoustic waves inside the pipelines finally by conducting length limited periodic drill string experiments it is shown that this model and algorithm can be used to obtain the acoustic wave spectrum distribution and impulse response characteristics inside periodic pipelines under operational conditions this method provides a theoretical basis for the fault diagnosis of acoustic wave transmission systems for oil industry applications

optimal control of infinite horizon partially observable decision processes modelled as generators of probabilistic regular languages decision processes with incomplete state feedback have been traditionally modelled as partially observable markov decision processes in this article we present an alternative formulation based on probabilistic regular languages the proposed approach generalises the recently reported work on language measure theoretic optimal control for perfectly observable situations and shows that such a framework is far more computationally tractable to the classical alternative in particular we show that the infinite horizon decision problem under partial observation modelled in the proposed framework is approximable and in general is not harder to solve compared to the fully observable case the approach is illustrated via two simple examples

applications of convex analysis within mathematics in this paper we study convex analysis and its theoretical applications we first apply important tools of convex analysis to optimization and to analysis we then show various deep applications of convex analysis and especially infimal convolution in monotone operator theory among other things we recapture the minty surjectivity theorem in hilbert space and present a new proof of the sum theorem in reflexive spaces more technically we also discuss autoconjugate representers for maximally monotone operators finally we consider various other applications in mathematical analysis

convergence of a hybrid algorithm for a reversible semigroup of nonlinear operators in banach spaces abstract the purpose of this paper is to study hybrid iterative schemes of halpern types for a semigroup t s s s of relatively nonexpansive mappings on a closed and convex subset c of a banach space with respect to a sequence n of asymptotically left invariant means defined on an appropriate invariant subspace of l s we prove that given a certain sequence n in 0 1 x c we can generate an iterative sequence x n which converges strongly to f x where f x is the generalized projection from c onto the fixed point set f our main result is even new for the case of a hilbert space

strong convergence of the cq method for fixed point iteration processes strong convergence theorems are obtained for the cq method for an ishikawa iteration process a contractive type iteration process for nonexpansive mappings and the proximal point algorithm for maximal monotone operators in hilbert spaces

a hybrid iteration scheme for equilibrium problems variational inequality problems and common fixed point problems in banach spaces abstract in this paper we introduce an iterative process which converges strongly to a common element of a set of common fixed points of finite family of closed relatively quasi nonexpansive mappings the solution set of generalized equilibrium problem and the solution set of the variational inequality problem for an inverse strongly monotone mapping in banach spaces

fixed point theorem for α nonexpansive mappings in banach spaces abstract we introduce the class of nonexpansive mappings in banach spaces this class contains the class of nonexpansive mappings and is related to the class of firmly nonexpansive mappings in banach spaces in addition we obtain a fixed point theorem for nonexpansive mappings in uniformly convex banach spaces

on reich s strong convergence theorems for resolvents of accretive operators let e be a real banach space with norm i then an operator a c e x e with domain d a and range r a is said to be accretive if xi xz 0 an accretive operator a c e x e is m accretive if r i ra e for all r 0 where z is the identity if a is accretive we can define for each positive r a singlevalued mapping j r z ra d a by j z ra it is called the resolvent of a in 6 reich proved the following theorem let e be a uniformly smooth banach space and let a c e x e be m accretive if 0 e r a then for each x in e the strong lim z x exists and belongs to a io he remarked also that the assumption that a is m accretive can be replaced with the assumption that cl a the closure of d a is convex and that a satisfies the range condition r z ra 1 cl d a for all r 0 in this paper we first prove a theorem that generalizes simultaneously the above results furthermore we generalize another reich strong convergence theorem asserting that the strong lim z x exists in uniformly convex and uniformly smooth banach spaces though our proofs are similar to those in 6 they are slightly simple on account of using banach limits

bisimulation through probabilistic testing abstract we propose a language for testing concurrent processes and examine its strength in terms of the processes that are distinguished by a test by using probabilistic transition systems as the underlying semantic model we show how a testing algorithm can distinguish with a probability arbitrarily close to one between processes that are not bisimulation equivalent we also show a similar result in a slightly stronger form for a new process relation called 2 3 bisimulation which lies strictly between that of simulation and bisimulation finally the ultimately strength of the testing language is shown to identify a new process relation called probabilistic bisimulation which is strictly stronger than bisimulation

ergodic theorems for hybrid sequences in a hilbert space with applications abstract in this paper we introduce the notion of generalized hybrid sequences extending the notion of nonexpansive sequences introduced and studied in our previous work djafari rouhani 1981 1990 1990 1997 2002 2004 2002 2 3 4 5 6 7 8 and prove ergodic and convergence theorems for such sequences in a hilbert space h subsequently we apply our results to prove new fixed point theorems for generalized hybrid mappings first introduced in kocourek et al 2010 14 takahashi and takeuchi 2011 20 defined on arbitrary nonempty subsets of h

a probabilistic language formalism for stochastic discrete event systems the formalism of probabilistic languages has been introduced for modeling the qualitative behavior of stochastic discrete event systems a probabilistic language is a unit interval valued map over the set of traces of the system satisfying certain consistency constraints regular language operators such as choice concatenation and kleene closure have been defined in the setting of probabilistic languages to allow modeling of complex systems in terms of simpler ones the set of probabilistic languages is closed under such operators thus forming an algebra it also is a complete partial order under a natural ordering in which the operators are continuous hence recursive equations can be solved in this algebra this is alternatively derived by using the contraction mapping theorem on the set of probabilistic languages which is shown to be a complete metric space the notion of regularity i e finiteness of automata representation of probabilistic languages has been defined and it is shown that regularity is preserved under choice concatenation and kleene closure we show that this formalism is also useful in describing system performance measures such as completion time reliability etc and present properties to aide their computation

supervisory control of probabilistic discrete event systems with recovery the authors discuss supervisory control of probabilistic discrete event systems supervisors for such systems will take probabilities of event occurrences into consideration in making control decisions the authors introduce a concept called spl epsiv containment of a given language and subsequently study its algebraic properties they discuss standard supervisor with only enablement disablement synthesis problems and reset supervisor with recovery mechanism synthesis problems for both fully observed and partially observed systems

ν a robot path planning algorithm based on renormalised measure of probabilistic regular languages this article introduces a novel path planning algorithm called that reduces the problem of robot path planning to optimisation of a probabilistic finite state automaton the algorithm makes use of renormalised measure of regular languages to plan the optimal path for a specified goal although the underlying navigation model is probabilistic the algorithm yields path plans that can be executed in a deterministic setting with automated optimal trade off between path length and robustness under dynamic uncertainties the algorithm has been experimentally validated on segway robotic mobility platforms in a laboratory environment

strong convergence theorems obtained by a generalized projections hybrid method for families of mappings in banach spaces abstract let c be a nonempty closed and convex subset of a uniformly convex and smooth banach space and let t n be a family of mappings of c into itself such that the set of all common fixed points of t n is nonempty we consider a sequence x n generated by the hybrid method by generalized projection in mathematical programming we give conditions on t n under which x n converges strongly to a common fixed point of t n and generalize the results given in 12 14 13 11

algebraic laws for nondeterminism and concurrency since a nondeterministic and concurrent program may in general communicate repeatedly with its environment its meaning cannot be presented naturally as an input output function as is often done in the denotational approach to semantics in this paper an alternative is put forth first a definition is given of what it is for two programs or program parts to be equivalent for all observers then two program parts are said to be observation congruent if they are in all program contexts equivalent the behavior of a program part that is its meaning is defined to be its observation congruence class the paper demonstrates for a sequence of simple languages expressing finite terminating behaviors that in each case observation congruence can be axiomatized algebraically moreover with the addition of recursion and another simple extension the algebraic language described here becomes a calculus for writing and specifying concurrent programs and for proving their properties

optimal supervisory control of probabilistic discrete event systems probabilistic discrete event systems pdes are modeled as generators of probabilistic languages and the supervisors employed are a probabilistic generalization of deterministic supervisors used in standard supervisory control theory in the case when there exists no probabilistic supervisor such that the behavior of a plant under control exactly matches the probabilistic language given as the requirements specification we want to find a probabilistic control such that the behavior of the plant under control is as close as possible to the desired behavior first as a measure of this proximity a pseudometric on states of generators is defined two algorithms for the calculation of the distance between states in this pseudometric are described then an algorithm to synthesize a probabilistic supervisor that minimizes the distance between generators representing the achievable and required behavior of the plant is presented

controlled markov chains with safety upper bound in this note we introduce and study the notion of safety control of stochastic discrete event systems dess modeled as controlled markov chains for nonstochastic dess modeled by state machines or automata safety is specified as a set of forbidden states or equivalently by a binary valued vector that imposes an upper bound on the set of states permitted to be visited we generalize this notion of safety to the setting of stochastic dess by specifying it as an unit interval valued vector that imposes an upper bound on the state probability distribution vector under the assumption of complete state observation we identify 1 the set of all state feedback controllers that satisfy the safety requirement for any given safe initial state probability distribution and 2 the set of all safe initial state probability distributions for a given state feedback controller

new monotone hybrid algorithm for hemi relatively nonexpansive mappings and maximal monotone operators the purpose of this article is to prove the strong convergence theorems for hemi relatively nonexpansive mappings in banach spaces in order to get the strong convergence theorems for hemi relatively nonexpansive mappings a new monotone hybrid iteration algorithm is presented and is used to approximate the fixed point of hemi relatively nonexpansive mappings noting that the general hybrid iteration algorithm can be used for relatively nonexpansive mappings but it can not be used for hemi relatively nonexpansive mappings however this new monotone hybrid algorithm can be used for hemi relatively nonexpansive mappings in addition a new method of proof has been used in this article that is by using this new monotone hybrid algorithm we firstly claim that the iterative sequence is a cauchy sequence the results of this paper modify and improve the results of matsushita and takahashi and some others

weak and strong convergence theorems for nonspreading type mappings in hilbert spaces abstract weak and strong convergence theorems are proved in real hilbert spaces for a new class of nonspreading type mappings more general than the class studied recently in kurokawa and takahashi y kurokawa w takahashi weak and strong convergence theorems for nonspreading mappings in hilbert spaces nonlinear anal 73 2010 1562 1568 we explored an auxiliary mapping in our theorems and proofs and this also yielded a strong convergence theorem of halpern s type for our class of mappings and hence resolved in the affirmative an open problem posed by kurokawa and takahashi in their final remark for the case where the mapping t is averaged

convergence theorems of shrinking projection methods for equilibrium problem variational inequality problem and a finite family of relatively quasi nonexpansive mappings we introduce a w mapping for a finite family of relatively quasi nonexpansive mappings and construct an iterative scheme for finding a common element of the solution set of equilibrium problem the solution set of the variational inequality problem for an inverse strongly monotone operator and set of common fixed points of a finite family of relatively quasi nonexpansive mappings strong convergence theorems are presented in a 2 uniformly convex and uniformly smooth banach space our results generalize and extend relative results

strong convergence of a proximal type algorithm in a banach space in this paper we study strong convergence of the proximal point algorithm it is known that the proximal point algorithm converges weakly to a solution of a maximal monotone operator but it fails to converge strongly then in math program 87 2000 pp 189 202 solodov and svaiter introduced the new proximal type algorithm to generate a strongly convergent sequence and established a convergence property for it in hilbert spaces our purpose is to extend solodov and svaiter s result to more general banach spaces using this we consider the problem of finding a minimizer of a convex function

iterative methods for strict pseudo contractions in hilbert spaces abstract let t i i 1 n be n strict pseudo contractions defined on a closed convex subset c of a real hilbert space h consider the problem of finding a common fixed point of these mappings and consider the parallel and cyclic algorithms for solving this problem we will prove the weak convergence of these algorithms moreover by applying additional projections we further prove that these algorithms can be modified to have strong convergence

strong convergence theorems for 2 generalized hybrid mappings in hilbert spaces abstract in this paper we prove a strong convergence theorem of halpern s type for 2 generalized hybrid mappings in a hilbert space we also deal with strong convergence theorems by hybrid methods for these nonlinear mappings in a hilbert space

strong convergence theorems by halpern mann iterations for relatively nonexpansive mappings in banach spaces abstract in this paper we modify halpern and mann s iterations for finding a fixed point of a relatively nonexpansive mapping in a banach space consequently a strong convergence theorem for a nonspreading mapping is deduced using a concept of duality theorems we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings finally we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a banach space

a mann type iterative scheme for variational inequalities in noncompact subsets of banach spaces abstract in this paper we study the existence of solutions and approximation of the solutions by using a mann type iterative scheme for variational inequalities in noncompact subsets of banach spaces the results presented in this paper generalize the corresponding results of j li j li on the existence of solutions of variational inequalities in banach spaces j math anal appl 295 2004 115 126

approximation of common fixed points for a countable family of relatively nonexpansive mappings in a banach space and applications abstract in this paper we prove a strong convergence theorem by the hybrid method for a countable family of relatively nonexpansive mappings in a banach space we also establish a new control condition for the sequence of mappings t n which is weaker than the control condition in lemma 3 1 of aoyama et al k aoyama y kimura w takahashi and m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in a banach space nonlinear anal 67 2007 2350 2360 moreover we apply our results for finding a common fixed point of two relatively nonexpansive mappings in a banach space and an element of the set of solutions of an equilibrium problem in a banach space respectively our results are applicable to a wide class of mappings

elasticity solution for stresses in a sandwich beam with functionally graded core introduction w eight savingsofferedby sandwich constructionsfor structures that require high bending stiffness are signi cant however sandwich constructions have not been fully exploited in structuralapplicationsdue to damage toleranceconcerns the core face sheet delamination is a major concern in sandwich construction the stiffness discontinuityat the face sheet and core interface results in a large increase in shear stresses although the core material itself may be able to withstand very high shear stresses the bond or adhesive layer at the interface could be relativelyweaker resulting in interfacial delamination results from this study indicate that the interfacial shear stresses can be reduced by varying functionallygrading the core properties through the thickness this note presents the displacement and stress elds in a functionallygraded core for a one dimensionalsandwichplate and compares them to that in a uniformcore the objective is to demonstrate the signi cant reduction in shear stresses at the face sheet core interface in the sandwich panel achieved by functionally grading the core properties

a hybrid scheme for finite families of equilibrium variational inequality and fixed point problems we introduce an iterative process for finding an element in the common fixed point set of finite family of closed relatively quasi nonexpansive mappings common solutions of finite family of equilibrium problems and common solutions of finite family of variational inequality problems for monotone mappings in banach spaces our theorem extends and unifies most of the results that have been proved for this important class of nonlinear operators

strong convergence theorem by a new hybrid method for equilibrium problems and variational inequality problems abstract in this paper we prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of the solutions of the variational inequality problem by using a new hybrid method we obtain a new result for finding a solution of an equilibrium problem and the solutions of the variational inequality problem

existence and approximation of fixed points of firmly nonexpansive type mappings in banach spaces a class of nonlinear operators in banach spaces is proposed we call each operator in this class a firmly nonexpansive type mapping this class contains the classes of firmly nonexpansive mappings in hilbert spaces and resolvents of maximal monotone operators in banach spaces we study the existence and approximation of fixed points of firmly nonexpansive type mappings in banach spaces

wave propagation of functionally graded layers treated by recursion relations and effective boundary conditions wave propagation through a layer of a material that is inhomogeneous in the thickness direction typically a functionally graded material fgm is investigated the material parameters and the displacement components are expanded in power series in the thickness coordinate leading to recursion relations among the displacement expansion functions these can be used directly in a numerical scheme as a means to get good field representations when applying boundary conditions and this can be done even if the layer is not thin this gives a schema that is much more efficient than the approach of subdividing the layer into many sublayers with constant material properties for thin layers for which the material parameters do not depend on the layer thickness the recursion relations can be used to eliminate all but the lowest order expansion functions employing the boundary conditions this leads to a set of effective boundary conditions relating the displacements and stresses on the two sides of the layer thus completely replacing the layer by these effective boundary conditions numerical examples illustrate the convergence properties of the scheme for fg layers and the influence of different variations of the material parameters in the fg layer

on some algorithms in banach spaces finding fixed points of nonlinear mappings abstract by using a modification of the hybrid method in mathematical programming we give some new algorithm to find out a fixed point of mappings which are in some sense non expansive our results hold in reflexive strictly convex smooth banach spaces with the kadec klee property