Abstract The aim of this article is to design a new iteration process for solving certain fixed-point problems. In particular, we prove weak and strong convergence theorems generalized nonexpansive mappings in the framework uniformly convex Banach spaces. addition, discuss stability solution under mild conditions. Further, provide some numerical examples indicate that proposed method works prop...

We discuss the following viscosity approximations with the weak contraction A for a nonexpansive mapping sequence {Tn}, yn αnAyn 1 − αn Tnyn, xn 1 αnAxn 1 − αn Tnxn. We prove that Browder’s and Halpern’s type convergence theorems imply Moudafi’s viscosity approximations with the weak contraction, and give the estimate of convergence rate between Halpern’s type iteration and Mouda’s viscosity ap...

The aim of this paper is to approximate fixed points nonexpansive type mappings in Banach spaces when the set nonempty. We study general Picard–Mann (GPM) algorithm, obtaining weak and strong convergence theorems. provide an example illustrate behaviour GPM algorithm. compare algorithm with other existing (well known) algorithms numerically (under different parameters initial guesses).

Assume that F is a nonlinear operator on a real Hilbert space H which is strongly monotone and Lipschitzian with constants η > 0 and κ > 0, respectively on a nonempty closed convex subset C of H . Assume also that C is the intersection of the fixed point sets of a finite number of nonexpansive mappings on H . We develop an implicit hybrid steepest-descent method which generates an iterative seq...

In this paper, we introduce a new iteration process for approximation of common fixed point of countably infinite family of nonself asymptotically nonexpansive mappings in uniformly convex Banach spaces, and prove weak and strong convergence of our iteration process to a common fixed point of these operators. Our theorems extend, generalize and unify many recently announced results. Our iterati...