Weak convergence of an iterative algorithm for accretive operators

Weak Convergence of Mann Iterative Algorithm for two Nonexpansive mappings

The mann fixed point algorithm play an importmant role in the approximation of fixed points of nonexpansive operators. In this paper, by considering new conditions, we prove the weak convergence of mann fixed point algorithm, for finding a common fixed point of two nonexpansive mappings in real Hilbert spaces. This results extend the privious results given by Kanzow and Shehu. Finally, we give ...

Weak Convergence of an Iterative Sequence for Accretive Operators in Banach Spaces

Let C be a nonempty closed convex subset of a smooth Banach space E and let A be an accretive operator of C into E. We first introduce the problem of finding a point u ∈ C such that 〈Au, J(v− u)〉 ≥ 0 for all v ∈ C, where J is the duality mapping of E. Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol’shteı̆n and Tret’yakov i...

Strong convergence of an iterative algorithm for accretive operators and nonexpansive mappings

In this paper, an iterative algorithm for finding a common point of the set of zeros of an accretive operator and the set of fixed points of a nonexpansive mapping is considered in a uniformly convex Banach space having a weakly continuous duality mapping. Under suitable control conditions, strong convergence of the sequence generated by proposed algorithm to a common point of two sets is estab...

A composite iterative algorithm for accretive and nonexpansive operators

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.

Strong Convergence of an Iterative Method for Inverse Strongly Accretive Operators