Convergence theorems for common fixed point of the family of nonself and nonexpansive mappings in real Banach spaces

In this paper, we construct cyclic-Mann type of iterative method for approximating a common fixed point of the finite family of nonself and nonexpansive mappings satisfying inward condition on a non-empty, closed and convex subset of a real uniformly convex Banach space . We also construct the averaging algorithm to the class of nonexpansive mappings in 2-uniformly smooth Banach space. We prove weak and strong convergence results for the iterative method. The results of this work extend results in the literature

CONVERGENCE OF SOME ITERATIVE METHODS FOR MONOTONE INCLUSION, VARIATIONAL INEQUALITY AND FIXED POINT PROBLEMS (Study on Nonlinear Analysis and Convex Analysis)

In this paper, we introduce two iterative methods (one implicit method and one explicit method) for finding a common element of the zero point set of a set-valued maximal monotone operator, the solution set of the variational inequality problem for a continuous monotone mapping, and the fixed point set of a continuous pseudocontractive mapping in a Hilbert space. Then we establish strong convergence of the proposed iterative methods to a common point of three sets, which is a solution of a certain variational inequality. Further, we find the minimum-norm element in common set of three sets. The main theorems develop and complement some well-known results in the literature

Moudafi's Viscosity Approximations with Demi-Continuous and Strong Pseudo-Contractions for Non-Expansive Semigroups

We consider viscosity approximation methods with demi-continuous strong pseudo-contractions for a non-expansive semigroup. Strong convergence theorems of the purposed iterative process are established in the framework of Hilbert spaces

Existence and Convergence Theorems by an Iterative Shrinking Projection Method of a Strict Pseudocontraction in Hilbert Spaces

The aim of this paper is to provide some existence theorems of a strict pseudocontraction by the way of a hybrid shrinking projection method, involving some necessary and sufficient conditions. The method allows us to obtain a strong convergence iteration for finding some fixed points of a strict pseudocontraction in the framework of real Hilbert spaces. In addition, we also provide certain applications of the main theorems to confirm the existence of the zeros of an inverse strongly monotone operator along with its convergent results

Convergence Theorem for a Family of Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces

Let be a real reflexive and strictly convex Banach space with a uniformly Gâteaux differentiable norm. Let ={()∶≥0} be a family of uniformly asymptotically regular generalized asymptotically nonexpansive semigroup of , with functions ,∶[0,∞)→[0,∞). Let ∶=()=∩≥0(())≠∅ and ∶→ be a weakly contractive map. For some positive real numbers and satisfying +>1, let ∶→ be a -strongly accretive and -strictly pseudocontractive map. Let {} be an increasing sequence in [0,∞) with lim→∞=∞, and let {} and {} be sequences in (0,1] satisfying some conditions. Strong convergence of a viscosity iterative sequence to common fixed points of the family of uniformly asymptotically regular asymptotically nonexpansive semigroup, which also solves the variational inequality ⟨(−),(−)⟩≤0, for all ∈, is proved in a framework of a real Banach space