Let E be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let J {T t : t ≥ 0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of E, with functions u, v : 0,∞ → 0,∞ . Let F : F J ∩t≥0F T t / ∅ and f : K → K be a weakly contractive map. For some positive real numbers λ and δ satisfying δ λ > 1, let G ...

Two iterative schemes for finding a common element of the set of zero points of maximal monotone operators and the set of fixed points of nonexpansive mappings in the sense of Lyapunov functional in a real uniformly smooth and uniformly convex Banach space are obtained. Two strong convergence theorems are obtained which extend some previous work. Moreover, the applications of the iterative sche...

Suppose C is a nonempty bounded closed convex retract of a real uniformly convex Banach space X with uniformly Gâteaux differentiable norm and P as a nonexpansive retraction of X onto C. Let T : C −→ X be an asymptotically nonexpansive nonself-map with sequence {kn}n≥1 ⊂ [1,∞), lim kn = 1, F (T ) = {x ∈ C : Tx = x}, and let u ∈ C. In this paper we study the convergence of the sequences {xn} and...

In a real uniformly convex and p-uniformly smooth Banach space, a modified forward-backward splitting iterative algorithm is presented, where the computational errors and the superposition of perturbed operators are considered. The iterative sequence is proved to be convergent strongly to zero point of the sum of infinite m-accretive mappings and infinite [Formula: see text]-inversely strongly ...

Let E be a real reflexive and strictly convex Banach space which has a uniformly Gâteaux differentiable norm and let C be a closed convex nonempty subset of E. Strong convergence theorems for approximation of a common zero of a countably infinite family of m-accretive mappings from C to E are proved. Consequently, we obtained strong convergence theorems for a countably infinite family of pseudo...

Suppose K is a closed convex subset of a real reflexive Banach space E which has a uniformly Gâteaux differentiable norm and every nonempty closed convex bounded subset of E has the fixed point property for nonexpansive mappings. We prove a strong convergence theorem for an m−accretive mapping from K to E. The results in this paper are different from the corresponding results in [8] and they im...

* Correspondence: [email protected] Department of Mathematics Education, Kyungnam University, Masan, Kyungnam, 631-701, Korea Full list of author information is available at the end of the article Abstract We study the strong convergence of a regularization proximal point algorithm for finding a common fixed point of a finite family of nonexpansive mappings in a uniformly convex and unifo...

Themain purpose of this paper is to introduce a new hybrid iterative scheme for finding a common element of set of solutions for a system of generalized mixed equilibrium problems, set of common fixed points of a family of quasi-φ-asymptotically nonexpansivemappings, and null spaces of finite family of γ-inverse strongly monotone mappings in a 2-uniformly convex and uniformly smooth real Banach...

In this paper, a new iterative scheme by hybrid method is constructed. Strong convergence of the scheme to a common element of the set of fixed points of an infinite family of relatively quasi-nonexpansive mappings and set of common solutions to a system of equilibrium problems in a uniformly convex real Banach space which is also uniformly smooth is proved. Our results extend important recent ...