limits of nonlinear discrete time control systems with fast subsystems we investigate the asymptotic properties of nonlinear discrete time control systems with fast subsystems in particular we use the averaging method in order to construct a limiting system for the slow subsystem we show continuous dependence of the slow trajectories on the perturbation parameter measuring the ratio of the different step sizes as a byproduct we get an exponential formula for the reachable set of nonlinear continuous time control systems with finite control range

nonlinear iteration semigroups of fuzzy cauchy problems in this paper we introduce an iteration semigroup of a nonlinear fuzzy valued function we show that the iterates converge and the limit function called the fuzzy exponential function is a solution to an autonomous fuzzy cauchy problem

subclasses of analytic functions associated with the generalized hypergeometric function using the generalized hypergeometric function we study a class f k p q s a b l of analytic functions with negative coefficients coefficient estimates distortion theorem extreme points and the radii of close to convexity and convexity for this class are given we also derive many results for the modified hadamard product of functions belonging to the class f k p q s a b l

inclusion properties of certain classes of meromorphic functions associated with the generalized hypergeometric function abstract the purpose of the present paper is to introduce several new classes of meromorphic functions defined by using a meromorphic analogue of the choi saigo srivastava operator for the generalized hypergeometric function and investigate various inclusion properties of these classes some interesting applications involving these and other classes of integral operators are also considered

the semigroup property of value functions in lagrange problems the lagrange problem in the calculus of variations exhibits the principle of optimality in a particularly simple form the binary operation of inf composition applied to the value functions of a lagrange problem equates the principle of optimality with a semigroup property this paper finds the infinitesimal generator of the semigroup by differentiating at t 0 the type of limit is epigraphical convergence in a uniform sense moreover the extent to which a semigroup is uniquely determined by its infinitesimal generator is addressed

a uniqueness theorem for differential inclusions abstract the reachable set multifunction of a lipschitz differential inclusion is characterized in terms of a semigroup property and a type of set differentiation at t 0 this generalizes the classical uniqueness theorem of ordinary differential equations a notion of an escape time for differential inclusions is introduced and plays a major role in the main result

on differential inclusions with prescribed attainable sets abstract in this article the inverse problem of the differential inclusion theory is studied for a given e 0 and a continuous set valued map t w t t t 0 where w t r n is compact and convex for every t t 0 it is required to define differential inclusion so that the hausdorff distance between the attainable set of the differential inclusion at the time moment t with initial set t 0 w t 0 and w t would be less than e for every t t 0

a c density theorem for differential inclusions with lipschitz continuous right hand sides abstract by definition solutions of differential inclusions are absolutely continuous functions with l 1 derivatives we prove that at least for a class of lipschitz continuous right hand sides the c solutions are dense in the set of all solutions with respect to the supremum norm

memoryless reconstruction of an extended state of a control delayed system the general feedback controller for a class of control variable delayed systems has recently been shown to be the general linear functional of an extended state of the system using only plant input output data this work formulates a memoryless observer for the reconstruction of this extended state it is also shown that the observer and the feedback controller can be independently designed in conformity with the separation principle

second order discrete approximations to strongly convex differential inclusions we present a runge kutta type scheme for discretization of strongly convex differential inclusions the accuracy of the approximation to the set of trajectories of the differential inclusion on a given interval is proven to be of second order with respect to the step length

on sandwich theorems for multivalent functions involving a generalized differential operator the purpose of this paper is to derive some subordination and superordination results for multivalent functions involving certain differential operator

on some applications of the briot bouquet differential subordination recently srivastava et al j dziok h m srivastava certain subclasses of analytic functions associated with the generalized hypergeometric function integral transforms spec funct 14 2003 7 18 j dziok h m srivastava classes of analytic functions associated with the generalized hypergeometric function appl math comput 103 1999 1 13 y c kim h m srivastava fractional integral and other linear operators associated with the gaussian hypergeometric function complex var theory appl 34 1997 293 312 introduced and studied a class of analytic functions associated with the generalized hypergeometric function in the present paper by using the briot bouquet differential subordination new results in this class are obtained

a linear operator and associated families of meromorphically multivalent functions making use of a linear operator which is defined here by means of the hadamard product or convolution the authors introduce and investigate the various properties and characteristics of two novel families of meromorphically multivalent functions they also extend the familiar concept of neighborhoods of analytic functions to these subclasses of meromorphically multivalent functions

certain inequality properties of multivalent analytic functions involving the dziok srivastava operator abstract the object of the present paper is to derive certain inequality properties of multivalent analytic functions involving the dziok srivastava operator

discrete approximations and fixed set iterations in banach spaces we study autonomous differential inclusions with right hand sides satisfying a one sided lipschitz osl condition in banach spaces with uniformly convex duals we first show that the solution set is closed and obtain estimates for euler type discrete approximations we then use these results to derive an analogue of the exponential formula for the reachable set as well as results regarding the existence and approximation of a strongly invariant attractor in the case of a negative osl constant as a by product conditions for controllability of the reverse time system are obtained

some inclusion relationships associated with dziok srivastava operator in this paper we introduce and study some new subclasses of p valent starlike convex close to convex and quasi convex functions defined by dziok srivastava operator inclusion relationships are established and integral operator of functions in these subclasses is discussed

functional observer and state feedback for input time delay systems the design of state functional observer and state feedback for systems with input time delays is addressed using the factorization approach in the frequency domain the design needs to achieve the loop transfer recovery of direct state feedback by using the functional observer based feedback control a necessary and sufficient condition is given for the existence of the state functional observers for such systems a parametrization for all observers of time delay systems is proposed based on the results of the parametrization the state functional observer and state feedback design procedure is presented the computation can be implemented in state space form using standard algorithms design examples are given to illustrate the procedure

inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators abstract by making use of a general linear operator i p a c the authors introduce several new subclasses of multivalent functions and investigate various inclusion relationships and argument properties associated with these subclasses some interesting applications involving such and other families of linear operators are also considered the results presented here include a number of known results as their special cases

stable transformations for control variable delayed systems a well known transformation containing a transport type integral induces a feedback controller for control variable delayed systems more recent numerical simulations based on the discretization of the transport type integral have cast doubt on the stabilizing property of this controller further investigation has revealed that the null space of the transport type integral is a potential source of a destabilizing input for the closed loop system this is the hidden input problem on the basis of the concept of a stable transformation a new feedback stabilizing controller is formulated to address the hidden input problem an additional benefit of the stable transformation theory is a quasi functional observer which allows the new feedback controller to be implemented as a constant multiple of an augmented state variable

extensions of clarke s proximal characterization for reachable mappings of differential inclusions in this paper we show that clarke s proximal characterization for reachable mappings of lipschitz continuous differential inclusions is valid for a larger class of continuous and locally one side kamke continuous inclusions we also give a new proximal characterization for reachable mappings of upper semi continuous differential inclusions

a new product integral representation for differential equations in separable banach spaces abstract letxbe a separable banach space consider the problem formula where the continuous functionf 0 x xis locally lipschitz continuous inx uniformly inton bounded intervals and continuous intuniformly w r t x the product integral formula x t lim n i 0 n i t n f i t n x 0 0 t t max for the solutionx t of d has been shown to converge we also show that iff t is lipschitz continuous onxwith constantl then the mappingx0 x t is lipschitz continuous with constanteltfor anyt 0 this formula has been recently developed for differential inclusions inrnby wolenski but the infinite dimensional case is considerably more involved

the exponential formula for the reachable set of a lipschitz differential inclusion the main goal of this paper is to prove a formula for the reachable set of a lipschitz differential inclusion with convex values the formula involves a kuratowski limit of sets that resembles a standard approach of defining the exponential of a matrix this explains the title the proof of the main theorem partially relies on a c 1 approximation result due to filippov for which a new proof is given a new approach of characterizing the value function associated with a mayer optimal control problem is given as an application

subordinations for analytic functions defined by the dziok srivastava linear operator in the present investigation we obtain certain sufficient conditions for a normalized analytic function f z defined by the dziok srivastava linear operator h l a1 to satisfy the certain subordination our results extend corresponding previously known results on starlikeness convexity and close to convexity

criteria for univalence of the dziok srivastava and the srivastava wright operators in the class a abstract in the geometric function theory gft much attention is paid to various linear integral operators mapping the class s of the univalent functions and its subclasses into themselves in 12 13 hohlov obtained sufficient conditions that guarantee such mappings for the operator defined by means of hadamard product with the gauss hypergeometric function in our earlier papers as 20 19 17 18 etc we extended his method to the operators of the generalized fractional calculus gfc 16 these operators have product functions of the forms m 1 f m and m 1 m and integral representations by means of the meijer g and fox h functions here we propose sufficient conditions that guarantee mapping of the univalent respectively of the convex functions into univalent functions in the case of the celebrated dziok srivastava operator 8 j dziok h m srivastava classes of analytic functions associated with the generalized hypergeometric function appl math comput 103 no 1 1999 pp 1 13 defined as a hadamard product with an arbitrary generalized hypergeometric function p f q similar conditions are suggested also for its extension involving the wright p q function and called the srivastava wright operator srivastava 36 since the discussed operators include the above mentioned gfc operators and many their particular cases operators of the classical fc from the results proposed here one can derive univalence criteria for many named operators in the gft as the operators of hohlov carlson and shaffer saigo libera bernardi erdelyi kober etc by giving particular values to the orders p q 1 of the generalized hypergeometric functions and to their parameters

differential inclusions with stable subinclusions wherexer te to t andf r x to t g r is a set valued mapping with compact and convex images an absolutely continuous function x m is a solution of 1 if it satisfies 1 for a e t e to t thus a differential inclusion generalizes an ordinary differential equation by permitting a set valued right hand side differential equations containing either control uncertain parameters or discontinuity in the right hand side can be transformed into the framework of 1 l 21 a well known and very useful result due to filippov 3 estimates the uniform distance from an arbitrary absolutely continuous function x to the set of solutions of 1 starting from x t by means of constant times the deviation

fixed set iterations for relaxed lipschitz multimaps abstract a dynamical system described by an autonomous differential inclusion with a right hand side satisfying a relaxed lipschitz condition as well as its euler approximations are studied we investigate the asymptotic properties of the solutions and of the attainable sets it is shown that the system has a strongly flow invariant set or a fixed set that is a set such that each trajectory starting from it does not leave it this set is also an attractor i e it attracts the continuous and the discrete euler trajectories as the time tends to infinity we give estimates of the rate of attraction an algorithm for approximating the fixed set by the attainable sets of the discrete system is also presented

proximal analysis and the minimal time function under general hypotheses on the target set s and the dynamics of the system we show that the minimal time function ts cdot is a proximal solution to the hamilton jacobi equation uniqueness results are obtained with two different kinds of boundary conditions a new propagation result is proven and as an application we give necessary and sufficient conditions for ts cdot to be lipschitz continuous near s a petrov type modulus condition is also shown to be sufficient for continuity of ts cdot near s

closed loop stability of a control variable delayed system a control variable delayed system is feedback transformed with a transformation induced feedback controller it is proved that the resulting closed loop system is stable if and only if the system open loop state matrix is stable this provides a theoretical basis for the numerical difficulties which have been observed in connection with the implementation of the above feedback controller

semigroups of relations and subdifferentials of the minimal time function and of the geodesic distance given a closed subset s of a banach space x we study the minimal time function to reach a point x of x starting from s we relate this problem to the study of the geodesic distance from x to s associated with a riemannian metric or a finsler metric it appears that both cases can be treated simultaneously and yield solutions to a hamilton jacobi equation we detect simple links between the general framework we propose and multivalued semigroups new concepts of infinitesimal generators of such semigroups are considered

properties of the reachable set of control systems abstract we investigate some properties of the reachable set of a control system representing the system as a differential inclusion and using proximal hamilton jacobi equation we describe its graph we work in infinitely dimensional hilbert space and use one sided lipschitz approach the funnel equation is considered in the last section that equation describes the reachable set in arbitrary banach space we consider also the autonomous case and prove the existence of a limit of the reachable set

a certain fractional derivative operator and its applications to a new class of analytic and multivalent functions with negative coefficients recently the authors made use of a certain operator of fractional derivatives in order to introduce and initiate a systematic study of a novel subclass tp of analytic and p valent functions with negative coefficients in this sequel to the aforementioned work they prove a number of closure and inclusion theorems and determine the radii of p valently close to convexity starlikeness and convexity for the class tp they also obtain a class preserving integral operator of the form f z j p z pz z0t 1 t dt p for the class studied here

a unified class of analytic functions involving a generalization of the srivastava attiya operator in this paper we present a unified class of analytic functions defined by a new convolution operator j p q b s a introduced recently by srivastava and gaboury 2014 which generalizes the well known srivastava attiya operator investigated by srivastava and attiya 2007 we derive coefficient inequalities growth and distortion theorems extreme points and fekete szego problem for this new function class

classes of analytic functions associated with the generalized hypergeometric function using the generalized hypergeometric function we introduce and study a class of analytic functions with negative coefficients coefficients estimates distortion theorems extreme points and the radii of convexity and starlikeness for this class are given relevant connections of these results with those in several earlier investigations are indicated

difference methods for differential inclusions a survey the main objective of this survey is to study convergence properties of difference methods applied to differential inclusions it presents in a unified way a number of results scattered in the li

on some applications of the dziok srivastava operator abstract carlson and shaffer b c carlson d b shaffer starlike and prestarlike hypergeometric functions siam j math anal 15 1984 737 745 have introduced a linear operator associated with the gaussian hypergeometric function which has been generalized by dziok and srivastava j dziok h m srivastava classes of analytic functions associated with the generalized hypergeometric function appl math comput 103 1999 1 13 certain classes of analytic functions defined by means of those operators have been considered in j dziok h m srivastava certain subclasses of analytic functions associated with the generalized hypergeometric function integral transform spec funct 14 2003 7 18 j dziok h m srivastava some subclasses of analytic functions with fixed argument of coefficients associated with the generalized hypergeometric function adv stud contemp math 5 2 2002 115 125 and recently in j dziok on some applications of the briot bouquet differential subordination j math anal appl 328 2007 295 301 j dziok some relations including various linear operators demonstratio math xl 2007 77 84 j l liu h m srivastava certain properties of the dziok srivastava operator appl math comput 159 2004 485 493 in the present paper new results for a familiar class of multivalent functions have been obtained we have used the methods of differential subordination and the properties of hadamard product

convolution properties for certain classes of multivalent functions abstract recently n e cho o s kwon and h m srivastava nak eun cho oh sang kwon h m srivastava inclusion relationships and argument properties for certain subclasses of multivalent functions associated with a family of linear operators j math anal appl 292 2004 470 483 have introduced the class s a c p h of multivalent analytic functions and have given a number of results this class has been defined by means of a special linear operator associated with the gaussian hypergeometric function in this paper we have extended some of the previous results and have given other properties of this class we have made use of differential subordinations and properties of convolution in geometric function theory

applications of multivalent prestarlike functions in the paper we introduce general classes of multivalent analytic functions defined by the subordination in particular we define the class of multivalent prestarlike functions by using the ruscheweyh s duality theory we investigate convolution properties related to multivalent prestarlike functions and various inclusion relationships between defined classes of functions some applications involving well known classes of functions defined by linear operators are also considered