resolution of singularities of threefolds in positive characteristic ii abstract together with vincent cossart olivier piltant resolution of singularities of threefolds in positive characteristic i reduction to local uniformization on artin schreier and purely inseparable coverings j algebra 320 3 2008 1051 1082 this article gives a complete proof of desingularization of quasiprojective varieties of dimensional 3 on fields which are differentially finite over perfect fields

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

strong convergence for the modified mann s iteration of λ strict pseudocontraction abstract in this paper for an strict pseudocontraction t we prove strong convergence of the modified mann s iteration defined by x n 1 n u n x n 1 n n n tx n 1 n x n where n n and n in 0 1 satisfy i 0 n k 2 with lim inf n n k 2 n 0 ii lim n n 0 and n 1 n iii lim sup n n 1 our results unify and improve some existing results

on projection algorithms for solving convex feasibility problems due to their extraordinary utility and broad applicability in many areas of classical mathematics and modern physical sciences most notably computerized tomography algorithms for solving convex feasibility problems continue to receive great attention to unify generalize and review some of these algorithms a very broad and flexible framework is investigated several crucial new concepts which allow a systematic discussion of questions on behaviour in general hilbert spaces and on the quality of convergence are brought out numerous examples are given

approximations for operating characteristics in a production inventory model with variable production rate this paper deals with production inventory control models with a variable production rate the demand process is a compound poisson process the production rate is controlled by the well known m m policy simple and accurate approximations are given for operating characteristics of the system it turns out that a sequential determination of m m and m yields a rule that minimizes average costs subject to a service level constraint numerical results are given to show the accuracy of the approximations

on sufficient conditions ensuring the norm convergence of an iterative sequence to zeros of accretive operators given two real sequences r n and n we study the iterative scheme x n 1 n u 1 n j r n x n for finding a zero of an accretive operator a where u is a fixed element and j r n denotes the resolvent of a to ensure its convergence the real sequence r n is always assumed to satisfy n 0 r n 1 r n in this paper we show this condition can be completely removed which enables us to improve a result recently obtained by saejung

a new sufficient condition for the strong convergence of halpern type iterations abstract the aim of this work is to give a new sufficient condition of the strong convergence of the halpern type iteration for a non expansive self mapping defined on a banach space with a uniformly g teaux differentiable norm several examples satisfying our condition are presented our results not only remove the restriction of the space with the fixed point property for non expansive self mappings but also get rid of the dependence on the convergence of the implicit anchor like continuous path z t in the proof

iteration processes for nonlinear mappings in convex metric spaces on considere le schema iteratif d ishikawa pour construire des points fixes d applications quasi contractives quasi contractives generalisees et quasi non dilatante dans des espaces metriques convexes

strong convergence theorems on an iterative method for a family of finite nonexpansive mappings abstract let e be either a strictly convex and reflexive banach spaces with a uniformly g teaux differentiable norm or a reflexive banach spaces with a weakly sequentially continuous duality mapping and k be a nonempty closed convex subset of e for a family of finite many nonexpansive mappings tl l 1 2 n and fixed contractive mapping f k k define iteratively a sequence xn as follows x n 1 n 1 f x n 1 n 1 t n 1 x n n 0 wheretn tn modn we proved that xn converges strongly to p f n 1 n f t n as n where p is the unique solution in f to the following variational inequality i f p j p u 0 for all u f t the main results presented in this paper generalized extended and improved the corresponding results of bauschke the approximation of fixed points of nonexpansive mappings in hilbert space j math anal appl 202 1996 150 159 halpen fixed points of nonexpansive maps bull amer math soc 73 1967 957 961 shioji and takahashi strong convergence of approximated sequences for nonexpansive mappings in banach spaces proc amer math soc 125 1997 3641 3645 wittmann approximation of fixed points of nonexpansive mappings arch math 59 1992 486 491 o hara et al iterative approaches to fineding nearest common fixed point of nonexpansive mappings in hilbert spaces nonlinear anal 54 2003 1417 1426 xu viscosity approximation methods for nonexpansive mappings j math anal appl 298 2004 279 291 jung iterative approaches to common fixed points of nonexpansive mappings in banach spaces j math anal appl 302 2005 509 520 zhou et al strong convergence theorems on an iterative method for a family of finite nonexpansive mappings in reflexive banach spaces appl math comput 173 1 2006 196 212 and others

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

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

strong convergence of an iterative method for nonexpansive and accretive operators abstract let x be a banach space and a an m accretive operator with a zero consider the iterative method that generates the sequence x n by the algorithm x n 1 n u 1 n j r n x n where n and r n are two sequences satisfying certain conditions and j r denotes the resolvent i r a 1 for r 0 strong convergence of the algorithm x n is proved assuming x either has a weakly continuous duality map or is uniformly smooth

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

new strong convergence theorems for nonexpansive nonself mappings without boundary conditions the aim of this work is to establish the strong convergence of explicit viscosity like methods for a nonexpansive nonself mapping without boundary conditions defined in a banach space this gets rid of the restriction and dependence on the implicit anchor like continuous path x t in the existing literature

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

optimal and simple approximate solutions to a production inventory system with stochastic and deterministic demand abstract we consider a continuous review production inventory system where demand is a mixture of a deterministic component and a random component which follows a compound poisson process demand is satisfied by a production facility which may be in production or idle while in production the facility produces at a constant rate a two number s s policy is used to control production when inventory reaches level s production is turned off and when inventory drops below level s production is turned on a level crossing approach is used to derive the steady state distribution of inventory level from which the exact total expected cost function consisting of setup inventory holding and backorder costs is determined the optimal s s policy can be found through a search of the expected cost function we propose approximations that give simple closed form solutions with near optimal performance

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

fixed point results for a generalized nonexpansive map in uniformly convex metric spaces abstract in this paper the existence of a unique fixed point of a map satisfying a very general contractive condition on a suitable subset of a uniformly convex metric space is proved this fixed point is approximated by averaging krasnosel skii iterations of a generalized nonexpansive map our results substantially improve and extend several known results existing in the literature

characteristic polyhedra of singularities without completion in hironaka j math kyoto univ 7 3 251 293 1967 defines characteristic polyhedra of a singularity embedded in spec r where r is a regular local ring unfortunately to build these polyhedra he must pick up coordinates in the completion widehat r in this article we show that in the hypersurface case whenever r is a g ring by using a different algorithm than hironaka s it is not necessary to extend r to compute the polyhedra

on optimal policies for production inventory systems with compound poisson demand and setup costs in this paper we consider a single item one machine production inventory system with compound poisson demand the production facility may be on or off while on the production rate is constant and while off the production rate is zero system costs consist of switching costs and inventory and backlogging costs we provide conditions when s s policies are optimal under the long run average expected cost criterion these conditions are met in particular but not necessarily when the inventory costs are convex the developed method in the proof is easy to apply to more general cases moreover the method allows us to compute optimal policies very efficiently

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

iterative approximation of fixed points of nonexpansive mappings let k be a nonempty closed convex subset of a real banach space e which has a uniformly g teaux differentiable norm and t k k be a nonexpansive mapping with f t x k tx x for a fixed 0 1 define s k k by sx 1 x tx x k assume that zt converges strongly to a fixed point z of t as t 0 where zt is the unique element of k which satisfies zt tu 1 t tzt for arbitrary u k let n be a real sequence in 0 1 which satisfies the following conditions c1 lim n 0 c2 n for arbitrary x0 k let the sequence xn be defined iteratively by xn 1 nu 1 n sxn then xn converges strongly to a fixed point of t

production inventory systems with lost sales and compound poisson demands this paper considers a continuous review single product production inventory system with a constant replenishment rate compound poisson demands and lost sales two objective functions that represent metrics of operational costs are considered 1 the sum of the expected discounted inventory holding costs and lost sales penalties both over an infinite time horizon given an initial inventory level and 2 the long run time average of the same costs the goal is to minimize these cost metrics with respect to the replenishment rate it is however not possible to obtain closed form expressions for the aforementioned cost functions directly in terms of positive replenishment rate prr to overcome this difficulty we construct a bijection from the prr space to the space of positive roots of lundberg s fundamental equation to be referred to as the lundberg positive rootlpr space this transformation allows us to derive closed form expressions for the aforementioned cost metrics with respect to the lpr variable in lieu of the prr variable we then proceed to solve the optimization problem in the lpr space and finally recover the optimal replenishment rate from the optimal lpr variable via the inverse bijection for the special cases of constant or loss proportional penalty and exponentially distributed demand sizes we obtain simpler explicit formulas for the optimal replenishment rate

the viscosity approximation process for quasi nonexpansive mappings in hilbert spaces in this paper we discuss the strong convergence of the viscosity approximation method in hilbert spaces relatively to the computation of fixed points of operators in the wide class of quasi nonexpansive mappings our convergence results improve previously known ones obtained for the class of nonexpansive mappings

approximation of common fixed points of a countable family of nonexpansive mappings in a banach space in this paper to find a common fixed point of a family of nonexpansive mappings we introduce a halpern type iterative sequence then we prove that such a sequence converges strongly to a common fixed point of nonexpansive mappings moreover we apply our result to the problem of finding a common fixed point of a countable family of nonexpansive mappings and the problem of finding a zero of an accretive operator

approximation of zeros of inverse strongly monotone operators in banach spaces abstract in this paper we consider the projection algorithm studied by iiduka and takahashi 2008 10 for finding a solution of the variational inequality problem for an inverse strongly monotone operator in a banach space we first remark that under the assumptions imposed on the operator in their paper the iterative sequence converges weakly to a zero of the operator not just a solution of the variational inequality problem in our proof slightly modified from the original we do not assume the uniform smoothness of a space as was the case there finally using halpern s type method we modify this algorithm to obtain the strong convergence to a zero of an inverse strongly monotone operator which is nearest to the initial element of the algorithm in the sense of the bergman distance associated with the function 1 2 2

the compensation method applied to a one product production inventory problem this paper considers a one product one machine production inventory problem demand requests for the product are governed by a poisson process with demand size being an exponential random variable the production facility may be in production or idle while in production the facility produces continuously at a constant rate the objective is to minimize system costs consisting of setup costs inventory holding costs and backorder costs given a two critical number policy the problem is analyzed as a constrained markov process using the compensation method a closed form expression is found for system cost as a function of the policy parameters this cost function may then be searched to find an optimal policy the production inventory problem is related to a server backlog process for an m m 1 system in which the server departs when the system empties and returns when the backlog exceeds a specified threshold the application of the compensation method to this server backlog process is discussed

halpern type proximal point algorithm of accretive operators abstract the main objectives of this paper are to employ a new proof technique to prove the strong convergence of x n and y n defined respectively by x n 1 n u n x n 1 n n j r n a x n and y n 1 n y n 1 n j r n a n u 1 n y n to some zero of accretive operator a in a uniformly convex banach space e with a uniformly g teaux differentiable norm or with a weakly continuous duality mapping j whenever n and n are sequences in 0 1 and r n 0 satisfying the conditions lim n n 0 n 1 n lim sup n n 1 lim inf n r n 0

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

on split common fixed point problems abstract based on the convergence theorem recently proved by the second author we modify the iterative scheme studied by moudafi for quasi nonexpansive operators to obtain strong convergence to a solution of the split common fixed point problem it is noted that moudafi s original scheme can conclude only weak convergence as a consequence we obtain strong convergence theorems for split variational inequality problems for lipschitz continuous and monotone operators split common null point problems for maximal monotone operators and moudafi s split feasibility problem

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

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

halpern s iteration in banach spaces abstract we prove strong convergence theorems for a sequence which is generated by halpern s iteration we also apply our result for finding zeros of an accretive operator our result improves the recent result of aoyama et al k aoyama y kimura w takahashi m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in a banach space nonlinear anal 67 2007 2350 2360 by removing some assumptions on the parameters finally we discuss the new sufficient condition studied by song y song a new sufficient condition for the strong convergence of halpern type iterations appl math comput 198 2 2008 721 728 y song new strong convergence theorems for nonexpansive nonself mappings without boundary conditions comput math appl 56 6 2008 1473 1478 and correct the main result of song and chai y song x chai halpern iteration for firmly type nonexpansive mappings nonlinear anal 71 10 2009 4500 4506

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

a single product cycling problem under brownian motion demand this paper treats a continuous review single product stochastic cycling problem with demand modelled as a brownian motion process a broad class of production policies is admitted they may be nonstationary non markovian or in fact almost arbitrary control theory is used to show that within this wide class of policies a simple stationary two number policy is optimal for the average cost minimization problem this policy switches production on when it is currently off and net inventory reaches a low critical level or switches it off when it is on and net inventory reaches a high critical level simple methods are developed for obtaining the optimal critical levels numerically examples are developed comparing the results with those given by graves and keilson for a different demand process having the same mean and variance per unit time

resolution of singularities of arithmetical threefolds ii abstract we prove grothendieck s conjecture on resolution of singularities for quasi excellent schemes x of dimension three and of arbitrary characteristic this applies in particular to x spec a a a reduced complete noetherian local ring of dimension three and to algebraic or arithmetical varieties of dimension three similarly if f is a number field a complete discretely valued field or more generally the quotient field of any excellent dedekind domain o any regular projective surface x f has a proper and flat model x over o which is everywhere regular

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

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

weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations abstract let h be a real hilbert space k a nonempty closed convex subset of h and t k k a lipschitz pseudocontraction with a nonempty fixed point set weak and strong convergence theorems for the iterative approximation of fixed points of t are proved furthermore if t h h is a lipschitz monotone operator and f r t where r t denotes the range of t weak and strong convergence theorems for the iterative approximation of solutions of the operator equation tx f are proved

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

unreliable production inventory model with a two phase erlang demand arrival process a production inventory system is studied in which an unreliable machine is susceptible to failure following which it must be repaired to make it operative again the demand for the product is governed by a two phase erlang process and demand sizes are independent and identically distributed random variables a two critical number policy m m is used to control a machine s setups and shutdowns namely the machine is shut down whenever the inventory level reaches m and is resumed to operate only when the inventory level falls below the critical number m m m we obtain the steady state distribution of the inventory process and some performance measures of the process

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 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

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

halpern iteration for firmly type nonexpansive mappings abstract the main aim of this paper is to study the strong convergence of halpern iteration for firmly type nonexpansive mappings defined on a banach space with a uniformly g teaux differentiable norm and the proof techniques are simpler and different from much existing literature also which gives the affirmative answer of the halpern open problem for this class of mapping

resolution of singularities of threefolds in positive characteristic i reduction to local uniformization on artin schreier and purely inseparable coverings abstract in dimension 3 the desingularization problem is reduced to local uniformization on artin schreier and purely inseparable coverings of regular space

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

the approximation of fixed points of compositions of nonexpansive mappings in hilbert space determining fixed points of nonexpansive mappings is a frequent problem in mathematics and physical sciences an algorithm for finding common fixed points of nonexpansive mappings in hilbert space essentially due to halpern is analyzed the main theorem extends wittmann s recent work and partially generalizes a result by lions algorithms of this kind have been applied to the convex feasibility problem