The purpose of this paper is to prove strong convergence theorems for common fixed points of two families of weak relatively nonexpansive mappings and a family of equilibrium problems by a new monotone hybrid method in Banach spaces. Because the hybrid method presented in this paper is monotone, so that the method of the proof is different from the original one. We shall give an example which i...

Approximate fixed point property problem for Mann iteration sequence of a nonexpansive mapping has been resolved on a Banach space independent of uniform (strict) convexity by Ishikawa [Fixed points and iteration of a nonexpansive mapping in a Banach space, Proc. Amer. Math. Soc. 59 (1976), 65–71]. In this paper, we solve this problem for a class of mappings wider than the class of asymptotical...

The purpose of this article is to initiate the notion monotone multivalued generalized (α,β)-nonexpansive mappings and explore iterative approximation fixed points for mapping in an ordered CAT(0) space. In particular, we employ S-iteration algorithm space prove some convergence results. Moreover, examples useful results related proposed are provided. Numerical experiments also provided illustr...

The asymptotically nonexpansive mappings have been introduced by Goebel and Kirk in 1972. Since then, a large number of authors have studied the weak and strong convergence problems of the iterative algorithms for such a class of mappings. It is well known that the asymptotically nonexpansive mappings is a proper subclass of the class of asymptotically pseudocontractive mappings. In the present...

Let K be a nonempty closed convex subset of a real reflexive Banach space X that has weakly sequentially continuous duality mapping Jφ for some gauge φ. Let Ti : K → K be a family of multivalued nonexpansive mappings with F := ∩∞i=0 F(Ti) ≠ ∅ which is a sunny nonexpansive retract of K with Q a nonexpansive retraction. It is our purpose in this paper to prove the convergence of two viscosity app...

Abridged English Version – Let (Ti)i∈I be a countable family of firmly nonexpansive mappings on a real Hilbert space H [i.e., (1) holds] and let F denote their set of common fixed points, which is assumed to be nonempty. In this Note we consider the problem (P) of finding a point in F . This generic problem arises in many branches of applied mathematics, e.g., solving systems of variational ine...

In this paper, we study M-iterative scheme in the new context of multi-valued generalized ?-nonexpansive mappings. A uniformly convex Banach space is used as underlying setting for our approach. We also provide a example ?-nonexpasive connect M iterative and other well known schemes with example, to show numerical efficiency results. Our results improve extend many existing current literature.

the purpose of this paper is to study the strong convergence of an implicit iteration process with errors to a common fixed point for a finite family of asymptotically pseudocontractive mappings and nonexpansive mappings in normed linear spaces. the results in this paper improve and extend the corresponding results of xu and ori, zhou and chang, sun, yang and yu in some aspects.

The purpose of this paper is to investigate the asymptotic behavior of algorithms for finding solutions for a certain class of variational inequalities V ID(C, I−f) involving nonexpansive type mappings in smooth Banach spaces. We study existence of solutions of variational inequalities V ID(C, I− f) when D is the set of solutions of zeros of accretive operators or the set of fixed points of non...

We introduce new iterative algorithms by hybrid method for finding a common element of the set of solutions of fixed points of infinite family of nonexpansive mappings, the set of common solutions of generalized mixed equilibrium problems, and the set of common solutions of the variational inequality with inverse-strongly monotone mappings in a real Hilbert space. We prove the strong convergenc...