a new completely general class of variational inclusions with noncompact valued mappings abstract in this paper we introduce and study a new completely general class of variational inclusions with noncompact valued mappings and construct some new iterative algorithms we prove the existence of solutions for the completely general class of variational inclusions and the convergence of iterative sequences generated by the algorithms

algorithm for generalized co complementarity problems in banach spaces abstract in this paper we introduce a new class of generalized co complementarity problems in banach spaces an iterative algorithm for finding approximate solutions of these problems is considered some convergence results for this iterative algorithm are derived and several existence results are obtained

a new class of generalized set valued implicit variational inclusions in banach spaces with an application in this paper we introduce and study a new class of generalized set valued implicit variational inclusions in real banach spaces by using nadler s theorem and the resolvent operator technique for m accretive mapping in real banach spaces we construct some new iterative algorithms for solving this class of generalized set valued implicit variational inclusions we prove the existence of solution for this kind of generalized set valued implicit variational inclusions without compactness and the convergence of iterative sequences generated by the algorithms in banach spaces we also give an application to generalized set valued implicit variational inequalities in real hilbert spaces

generalized variational inclusions and generalized resolvent equations in banach spaces in this paper we introduce and study generalized variational inclusions and generalized resolvent equations in real banach spaces it is established that generalized variational inclusion problems in uniformly smooth banach spaces are equivalent to fixed point problems we also establish a relationship between generalized variational inclusions and generalized resolvent equations by using nadler s fixed point theorem and resolvent operator technique for m accretive mappings in real banach spaces we propose an iterative algorithm for computing the approximate solutions of generalized variational inclusions the iterative algorithms for finding the approximate solutions of generalized resolvent equations are also proposed the convergence of approximate solutions of generalized variational inclusions and generalized resolvent equations obtained by the proposed iterative algorithms is also studied our results are new and represent a significant improvement of previously known results some special cases are also discussed

perturbed proximal point algorithms for generalized quasivariational inclusions abstract in this paper we study a class of generalized quasivariational inclusions by using the properties of the resolvent operator associated with a maximal monotone mapping in hilbert space we have established an existence theorem of solutions for generalized quasivariational inclusions suggesting a new iterative algorithm and a perturbed proximal point algorithm for finding approximate solutions which strongly converge to the exact solution of the generalized quasivariational inclusions as special cases some known results in this field are also discussed

the category o for a general coxeter system abstract we study the category o for a general coxeter system using a formulation of fiebig the translation functors the zuckerman functors and the twisting functors are defined we prove the fundamental properties of these functors the duality of zuckerman functor and generalization of verma s result about homomorphisms between verma modules

a perturbed algorithm for variational inclusions a perturbed method for solving a new class of variational inclusions is presented and a convergence result which includes as a special case some known results in this field is given

generalized set valued variational inclusions in banach spaces in this paper a generalization and improvement of noor s theorem for generalized set valued variational inclusion in real banach spaces is studied the results presented in this paper generalize improve and unify a number of recent results

on the existence and iterative approximation problems of solutions for set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions in banach spaces by using michael s selection theorem and nadler s theorem some existence theorems and iterative algorithms for solving this kind of set valued variational inclusion in banach spaces are established and suggested

set valued variational inclusions in banach spaces the purpose of this paper is to introduce and study a class of set valued variational inclusions without compactness condition in banach spaces by using michael s selection theorem and nadler s theorem an existence theorem and an iterative algorithm for solving this kind of set valued variational inclusions in banach spaces are established and suggested

minimal entropy of states emerging from noisy quantum channels we consider the minimal entropy of qubit states transmitted through two uses of a noisy quantum channel which is modeled by the action of a completely positive trace preserving or stochastic map we provide strong support for the conjecture that this minimal entropy is additive namely that the minimum entropy can be achieved when product states are transmitted explicitly we prove that for a tensor product of two unital stochastic maps on qubit states using an entanglement that involves only states which emerge with minimal entropy cannot decrease the entropy below the minimum achievable using product states we give a separate argument based on the geometry of the image of the set of density matrices under stochastic maps which suggests that the minimal entropy conjecture holds for nonunital as well as for unital maps we also show that the maximal norm of the output states is multiplicative for most product maps on n qubit states including all those for which at least one map is unital for the class of unital channels on c sup 2 we show that additivity of minimal entropy implies that the holevo see ieee trans inform theory vol 44 p 269 73 1998 and russian math surv p 1295 1331 1999 capacity of the channel is additive over two inputs achievable with orthogonal states and equal to the shannon capacity this implies that superadditivity of the capacity is possible only for nonunital channels

on a new system of generalized mixed quasi variational like inclusions involving a η m accretive operators with applications in this paper we introduce a new and interesting system of generalized mixed quasi variational like inclusions with a h m accretive operators and relaxed cocoercive mappings which contains variational inequalities variational inclusions systems of variational inequalities systems of variational like inequalities and systems of variational inclusions in the literature as special cases by using the resolvent technique for the a h m accretive operators we prove the existence of solutions and the convergence of a new p step iterative algorithm for this system of generalized mixed quasi variational like inclusions in real q uniformly smooth banach spaces the results in this paper unifies extends and improves some known results in the literature

generalized set valued variational inclusions and resolvent equations in this paper we establish the equivalence between the generalized set valued variational inclusions the resolvent equations and the fixed point problem using the resolvent operator technique this equivalence is used to suggest and analyze some iterative algorithms for solving the generalized set valued variational inclusions and related optimization problems

an algorithm based on resolvent operators for solving variational inequalities in hilbert spaces abstract in this paper a new monotonicity m monotonicity is introduced and the resolvent operator of an m monotone operator is proved to be single valued and lipschitz continuous with the help of the resolvent operator an equivalence between the variational inequality vi c f g and the fixed point problem of a nonexpansive mapping is established a proximal point algorithm is constructed to solve the fixed point problem which is proved to have a global convergence under the condition that f in the vi problem is strongly monotone and lipschitz continuous furthermore a convergent path newton method which is based on the assumption that the projection mapping c is semismooth is given for calculating e solutions to the sequence of fixed point problems enabling the proximal point algorithm to be implementable

normal maps inducted by linear transformations we study a certain piecewise linear manifold which we call the normal manifold associated with a polyhedral convex set and a family of continuous functions called normal maps that are induced on this manifold by continuous functions from rn to rn these normal maps occur frequently in optimization and equilibrium problems and the subclass of normal maps induced by linear transformations plays a key role our main result is that the normal map induced by a linear transformation is a lipschitzian homeomorphism if and only if the determinant of the map in each n cell of the normal manifold has the same nonzero sign

finite size mean field models we characterize the two site marginals of exchangeable states of a system of quantum spins in terms of a simple positivity condition this result is used in two applications we first show that the distance between two site marginals of permutation invariant states on n spins and exchangeable states is of order 1 n the second application relates the mean ground state energy of a mean field model of composite spins interacting through a product pair interaction with the mean ground state energies of the components

a de finetti representation for finite symmetric quantum states consider a symmetric quantum state on an n fold product space that is the state is invariant under permutations of the n subsystems we show that conditioned on the outcomes of an informationally complete measurement applied to a number of subsystems the state in the remaining subsystems is close to having product form this immediately generalizes the so called de finetti representation to the case of finite symmetric quantum states

approximation solvability of nonlinear random a η resolvent operator equations with random relaxed cocoercive operators in this paper we introduce and study a new class of nonlinear random a h resolvent operator equations with random relaxed cocoercive operators in hilbert spaces by using chang s lemma theorem 3 1 of liu and li and the resolvent operator technique for a h monotone operators due to lan we also prove the existence theorems of the solutions and convergence theorems of the new generalized random iterative procedures with errors for this nonlinear random a h resolvent operator equations involving non monotone random set valued operators in hilbert spaces the results presented in this paper improve and generalize some known corresponding results in the literature

perturbed algorithms and sensitivity analysis for a general class of variational inclusions in the present paper we study a perturbed iterative method for solving a general class of variational inclusions an existence result which generalizes some known results in this field a convergence result and a new iterative method are given we also prove the continuity of the perturbed solution to a parametric variational inclusion problem several special cases are discussed

an algorithm for a class of quasivariational inequalities abstract in the present paper we study the convergence of an algorithm for a class of quasivariational inequalities modelling contact problems with friction in elastostatics

mann and ishikawa type perturbed iterative algorithms for generalized nonlinear implicit quasi variational inclusions abstract in this paper we introduce a new class of generalized nonlinear implicit quasi variational inclusions and prove its equivalence with a class of fixed point problems by making use of the properties of maximal monotone we also prove the existence of solutions for this generalized nonlinear implicit quasi variational inclusions and the convergence of iterative sequences generated by the perturbed algorithms

the studies of systems of variational inclusions problems and variational disclusions problems with applications abstract in this paper we study existence theorems of solutions for systems of variational inclusions problems and systems of variational disclusions problems from these existence results we establish existence theorems of solutions for systems of generalized vector quasiequilibrium problems and systems of quasioptimization problems