[PDF] Top 20 On the Weak Relatively Nonexpansive Mappings in Banach Spaces

... of weak relatively nonexpansive mapping has been presented and studied by many authors 5–8, but they have not given the example which is weak relatively nonexpansive mapping but ... See full document

... of mappings called Bregman weak relatively nonexpansive mappings and propose new hybrid iterative algorithms for finding common fixed points of an infinite family of such mappings ... See full document

... weakly relatively nonexpansive map- pings introduced in the present paper is different from the class of Bregman weak relatively nonexpansive mappings introduced in ...a ... See full document

... alizes the result of Matsushita and Takahashi [12]. If E is a Hilbert space and each T i is a nonexpansive mapping from C into itself, then J is the identity operator on E, and hence (1.5) and (1.7) are coincident ... See full document

... for all x, y, z ∈ E. Let E be a strictly convex, smooth, and reflexive Banach space, and let J be the duality mapping from E into E ∗ . Then J −1 is also single-valued, one-to-one, and surjective, and it is the ... See full document

... Recently, many iteration processes were introduced by mathematicians for finding a common element of the set of fixed points of a nonlinear mapping and the solution set of an equilibrium problem in the framework of ... See full document

... smooth Banach space has a uniformly Gˆateaux differentiable norm and is such that every nonempty closed convex and bounded subset of X has the fixed point property for nonexpansive ...real Banach ... See full document

... asymptotically nonexpansive mappings (or nonexpansive mappings) in Hilbert spaces or uniformly convex Banach spaces have been considered by several authors (see, ... See full document

... and weak convergence theorems with the help of his process for the class of nonexpansive mappings in general Banach spaces and apply it to obtain a result in uniformly convex ... See full document

... metric spaces has been ini- tiated by Ran and Reurings [] for finding applications to matrix ...nondecreasing mappings and presented an application to differential ...ordered Banach spaces and ... See full document

... As we all know that if C is a nonempty closed convex subset of a Hilbert space H and P C : H → C is the metric projection of H onto C, then P C is nonexpansive. This fact actually characterizes Hilbert ... See full document

... Huang, Strong convergence theorems for fixed point problems and generalized equilibrium problems of three relatively quasi-nonexpansive mappings in Banach spaces, J.. Zhou, Approximate p[r] ... See full document

... Motivated by Chuang et al. [] and Nilsrakoo and Saejung [], we present the modified Halpern-type iterative method for finding a common element of the fixed point set of a relatively nonexpansive mapping and ... See full document

... Panyanak, Nonexpansive set-valued mappings in metric and Banach spaces,. Nonlinear Convex Anal[r] ... See full document

... asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in ...the weak and strong convergence problems of the iterative algorithms for such a class of ...asymptotically ... See full document

... of designing and analyzing feasibility and optimization algorithms. This opened a growing area of research in which Bregman’s technique is applied in various ways in order to design and analyze iterative algorithms for ... See full document

... (see a counterexample in []; see also [, ]). Some attempts to modify the Mann iteration method (.) so that strong convergence is guaranteed have recently been made. Bauschke and Combettes [] proposed another ... See full document

... exists. In this case, X is called smooth. The norm of Banach space X is said to be Fréchet differentiable if for each x Î S(X), limit (1.1) is attained uniformly for y Î S(X) and the norm is uniformly Fréchet ... See full document

... of relatively nonexpansive mappings in a Banach ...a relatively nonexpansive mapping and the solution set of an equilibrium problem are also ... See full document

... Proof. Let α n = λ for each n ∈ N ∪ { 0 } . It is clear that lim inf n →∞ α n (1 − α n ) = λ(1 − λ) > 0. We show that if T is nonexpansive, then T is relatively nonexpansive. It is obvious that ... See full document