[PDF] Top 20 Variational relation problems: existence of solutions and fixed points of contraction mappings

... linear variational relation ...linear variational problem may have no solutions (see Example ...an existence condition for this ... See full document

... 12 R. Wangkeeree and R. Wangkeeree, “Strong convergence of the iterative scheme based on the extragradient method for mixed equilibrium problems and fixed point problems of an infinite family of ... See full document

... the existence of fixed points for common fixed point ...point problems, systems of common fixed point problems and common fixed point problems without convex ...set-valued ... See full document

... generalized variational inequali- ties are useful and important extension and generalizations of the variational inequalities with a wide range of applications in industry, mathematical finance, economics, ... See full document

... Banach contraction principle from single-valued mappings to multivalued mappings and proved the existence of fixed points for contractive multivalued mappings in complete metric ... See full document

... of variational relation ...set-valued mappings with nonempty values, and R(x, y, z), Q(y, x, z) be two relations linking elements x ∈ X, y ∈ Y and z ∈ ...of variational relation ... See full document

... nonexpansive mappings in a Hilbert spaces without using the W-mapping generated by a family of infinitely (finitely) nonexpansive ...of solutions of a generalized equili- brium problem, the set of ... See full document

... a contraction of H into itself with coefficient β ∈ 0, 1, and B is a strongly positive bounded linear operator with coefficient γ and 0 < γ < ...of mappings defined as Lemma ... See full document

... equilibrium problems are unified models of several prob- lems, namely, optimization problems, saddle point problems, variational inequalities, fixed point problems, Nash equilibrium ... See full document

... common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings,” Nonlinear Analysis: Theory, ... See full document

... Corollary 3.3. Let H be a real Hilbert space, T : H → H, G : H → H a nonexpansive map and an η- strongly monotone map which is also κ-Lipschitzian, respectively. For λ, σ ∈ 0, 1 and δ ∈ 0, 2η/κ 2 , define a map T λ : H → ... See full document

... of solutions of systems of equilibrium problems and the set of common fixed points of a sequence of nonexpansive mappings and a representation of nonexpansive ...a variational ... See full document

... set-valued mappings satisfying a Caristi-type condition which complement the results in ...the existence of a fixed point for such mappings assuming that their graphs are ... See full document

... Let X be an arbitrary nonempty set. A fixed point for a self-mapping T : X → X is a point x ∈ X such that Tx = x. The applications of fixed point theory are very important in diverse disciplines of mathematics, statistics, ... See full document

... Alber and Guerre- Delabriere[2] defined the concept of weakly contractive mapping on Hilbert spaces and proved the existence of fixed points. Rhoades [11] showed that most re- sults of Alber and ... See full document

... non-self mappings sa- tisfying certain  -contractive condition was constructed, and then that the limit of the sequence is the unique common fixed point of the mappings was ...type fixed ... See full document

... The existence, uniqueness, and iterative approximations of fixed points for four classes of contractive mappings of integral type in complete metric spaces are ...many points are also ... See full document

... The purpose of this article is to study the equivalence between some kinds of impli- cit and explicit iterative approximations approximations. As applications, we utilize our results to study some approximation ... See full document

... Let E be a reflexive Banach space with a uniformly Gˆateaux differentiable norm. Suppose that every weakly compact convex subset of E has the fixed point property for nonexpansive mappings. Let C be a ... See full document

... In this paper, we study fixed points of quasi-contraction mappings in a cone metric space (X, d) over a solid vector space (Y , ). Cone metric spaces have a long history (see Col- latz [], Zabrejko ... See full document