in this paper we introduce new modified implicit and explicit algorithms and prove strong convergence of the two algorithms to a common fixed point of a family of uniformly asymptotically regularasymptotically nonexpansive mappings in a real reflexive banach space with a uniformly g$hat{a}$teaux differentiable norm. our result is applicable in $l_{p}(ell_{p})$ spaces,$1 < p

The notion of a bead metric space is defined as a nice generalization of the uniformly convex normed space such as $CAT(0)$ space, where the curvature is bounded from above by zero. In fact, the bead spaces themselves can be considered in particular as natural extensions of convex sets in uniformly convex spaces and normed bead spaces are identical with uniformly convex spaces. In this paper, w...

Mean nonexpansive mappings were first introduced in 2007 by Goebel and Japón Pineda and advances have been made by several authors toward understanding their fixed point properties in various contexts. For any given mean nonexpansive mapping of a Banach space, many of the positive results have been derived from knowing that a certain average of some iterates of the mapping is nonexpansive. Howe...

*Correspondence: [email protected] 1Department of Economics, Chiba University, Yayoi-cho, Inage-ku, Chiba-shi, Chiba, 263-8522, Japan Full list of author information is available at the end of the article Abstract We show that a strongly relatively nonexpansive sequence of mappings can be constructed from a given sequence of firmly nonexpansive-like mappings in a Banach space. Using this ...

There are two important connections between the classes of nonexpansive and of accretive mappings which give rise to a strong connection between the fixed point theory of nonexpansive mappings and the mapping theory of accretive maps. These are: (1) If U is a nonexpansive mapping of D(U) into X, and if we set T — I--U, D(T)=D(U), then T is an accretive mapping of D{T) into X. (2) If { U(i)f t^O...

and Applied Analysis 3 where J is the duality mapping from E into E∗. It is well known that if C is a nonempty closed convex subset of a Hilbert space H and PC : H → C is the metric projection of H onto C, then PC is nonexpansive. This fact actually characterizes Hilbert spaces and consequently, it is not available in more general Banach spaces. It is obvious from the definition of function φ t...

It is shown that any A-firmly, 0 < A < 1 , nonexpansive mapping T: C —> C has a fixed point in C whenever C is a finite union of nonempty, bounded, closed convex subsets of a uniformly convex Banach space. Let C be a nonempty subset of a Banach space X, and let X £ (0, 1). Then a mapping T: C —> X is said to be X-firmly nonexpansive if (1) \\Tx Ty\\ < ||(1 X)(x y)+X(Tx Ty)\\ for all x, y £ C. I...

We introduce an iterative process which converges strongly to a common point of solution of variational inequality problem for a monotone mapping and fixed point of uniformly Lipschitzian relatively asymptotically nonexpansive mapping in Banach spaces. As a consequence, we provide a scheme that converges strongly to a common zero of finite family of monotone mappings under suitable conditions. ...