In this paper, we prove a strong convergence theorem for fixed points of sequence for multivalued nonexpansive mappings and a zero of maximal monotone operator in Banach spaces by using the hybrid projection method. Our results modify and improve the recent results in the literatures.

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.

The problem of finding a minimizer of the sum of two convex functions — or, more generally, that of finding a zero of the sum of two maximally monotone operators — is of central importance in variational analysis. Perhaps the most popular method of solving this problem is the Douglas–Rachford splitting method. Surprisingly, little is known about the range of the Douglas–Rachford operator. In th...

‎Our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove a strong convergence theorem for approximating a solution of split equality fixed point problem for quasi-nonexpansive mappings in a real Hilbert space‎. ‎So many have used algorithms involving the operator norm for solving split equality fixed point problem‎, ‎...

Let $X$ be a reflexive Banach space, $T:Xto X$ be a nonexpansive mapping with $C=Fix(T)neqemptyset$ and $F:Xto X$ be $delta$-strongly accretive and $lambda$- strictly pseudocotractive with $delta+lambda>1$. In this paper, we present modified hybrid steepest-descent methods, involving sequential errors and functional errors with functions admitting a center, which generate convergent sequences ...

The problem of finding a fixed point to a nonexpansive operator is an abstraction of many models in numerical linear algebra, optimization, and other areas of scientific computing. To solve this problem, we propose ARock, an asynchronous parallel algorithmic framework, in which a set of agents (machines, processors, or cores) update randomly selected coordinates of the unknown variable in an as...

In this paper, an iterative scheme for finding common solutions of the set fixed points a pair asymptotically quasi-nonexpansive mapping and minimizers minimization problem is constructed. Using idea jointly demicloseness principle, strong convergence results are achieved without imposing any compactness condition on space or operator. Our improve, extend generalize many important in literature.

Let H be a real Hilbert space, let S, T be two nonexpansive mappings such that F S ∩ F T / ∅, let f be a contractive mapping, and let A be a strongly positive linear bounded operator on H. In this paper, we suggest and consider the strong converegence analysis of a new two-step iterative algorithms for finding the approximate solution of two nonexpansive mappings as xn 1 βnxn 1 − βn Syn, yn αnγ...

Given a finite family of nonexpansive self-mappings of a Hilbert space, a particular quadratic functional, and a strongly positive selfadjoint bounded linear operator, Yamada et al. defined an iteration scheme which converges to the unique minimizer of the quadratic functional over the common fixed point set of the mappings. In order to obtain their result, they needed to assume that the maps s...