where 〈·, ·〉 denotes the generalized duality pairing. A Banach space E is said to be strictly convex if ‖ x y /2‖ < 1 for all x, y ∈ E with ‖x‖ ‖y‖ 1 and x / y. It is said to be uniformly convex if limn→∞‖xn − yn‖ 0 for any two sequences {xn} and {yn} in E such that ‖xn‖ ‖yn‖ 1 and limn→∞‖ xn yn /2‖ 1. Let UE {x ∈ E : ‖x‖ 1} be the unit sphere of E. Then the Banach space E is said to be smooth ...

In this paper, we introduce a new iterative procedure which is constructed by the modified block hybrid projection method for solving a common solution of fixed point problems for two countable families of uniformly total quasi-φ-asymptotically nonexpansive and uniformly Lipschitz continuous mappings. Under suitable conditions, some strong convergence theorems are established in a uniformly smo...

The purpose of this paper is to give a regularization method to obtain the strong convergence of iterative sequence to a solution of the problem of finding a common fixed point of a finite family nonexpansive mappings in an uniformly convex and uniformly smooth Banach space.

In this paper, we propose a one-step composite iterative algorithm for solving operator equations involving accretive and nonexpansive operators. We obtain a weak convergence theorem for these nonlinear operators in the framework of 2-uniformly smooth and uniformly convex Banach space. c ©2017 All rights reserved.

We introduce an iterative algorithm for finding a common minimum norm fixed point of a finite family of asymptotically nonextensive nonself mappings. A strong convergence theorem of common element is established in a uniformly smooth and uniformly convex Banach space. Mathematics Subject Classification: 47H09; 47H05

The purpose of this paper is to solve the hierarchical variational inequality with the constraint of a general system of variational inequalities in a uniformly convex and 2-uniformly smooth Banach space. We introduce implicit and explicit iterative algorithms which converge strongly to a unique solution of the hierarchical variational inequality problem. Our results improve and extend the corr...

A new hybrid projection algorithm is considered for a finite family of λi-strict pseudocontractions. Using the metric projection, some strong convergence theorems of common elements are obtained in a uniformly convex and 2-uniformly smooth Banach space. The results presented in this paper improve and extend the corresponding results of Matsushita and Takahshi, 2008, Kang and Wang, 2011, and man...

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

and Applied Analysis 3 It is known that a uniformly convex Banach space is reflexive and strictly convex. The function δ : 0, 2 → 0, 1 which is called the modulus of convexity of E is defined as follows: δ ε inf {