The class of strictly pseudo-contractive mappings is known to have more powerful applications than the nonexpansive in solving nonlinear equations such as inverse and equilibrium problems. Motivated by potency mappings, a generalized viscosity implicit algorithm constructed for finding their fixed points framework Banach spaces. strong convergence newly sequence point mapping obtained under som...

In this paper, we study the convergence of implicit Mann iteration processes with bounded perturbations for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain the -convergence results of implicit Mann iteration schemes with bounded perturbations for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the s...

The purpose of this article is to prove strong convergence theorems for fixed points of closed hemirelatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive m...

Let C be a nonempty closed convex subset of a Hilbert spaceH, T a self-mapping of C. Recall that T is said to be nonexpansive if ‖Tx − Ty‖ ≤ ‖x − y‖, for all x, y ∈ C. Construction of fixed points of nonexpansive mappings via Mann’s iteration 1 has extensively been investigated in literature see, e.g., 2–5 and reference therein . But the convergence about Mann’s iteration and Ishikawa’s iterati...

A point x ∈ C is a fixed point of T provided Tx = x. Denote by F(T) the set of fixed points of T ; that is, F(T)= {x ∈ C : Tx = x}. It is assumed throughout the paper that T is a nonexpansive mapping such that F(T) =∅. One classical way to study nonexpansive mappings is to use contractions to approximate a nonexpansive mapping [1, 9]. More precisely, take t ∈ (0,1) and define a contraction Tt :...

The purpose of this paper is to study strong and ∆ - convergence a newly defined iteration common fixed point two asymptotically nonexpansive self mappings in hyperbolic space framework. We provide an example comparison table support our assertions.

In this paper, we introduce an iteration process for approximating common fixed points of two nonself asymptotically nonexpansive mappings in Banach spaces. Our process contains Mann iteration process and some other processes for nonself mappings but is independent of Ishikawa iteration process. We prove some weak and strong convergence theorems for this iteration process. Our results generaliz...

In this paper, we prove some strong and weak convergence theorems using a modified iterative process for nonself asymptotically nonexpansive mappings in a uniformly convex Banach space. This will improve and generalize the corresponding results in the existing literature. Finally, we will state that our theorems can be generalized to the case of finitely many mappings. c © 2007 Elsevier Ltd. Al...

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces. 1. Introduction and preliminaries. Let D be a nonempty subset of a real Banach space X and T : D → D a nonlinear mapping. The mapping T is said to be asymptotically quasi-nonexpansive (see [5]) if F(T) = ∅ and there exists a sequence {k n } in [0, ∞) with lim n...

Abstract The purpose of this short note is to present a correction the proof main result given in paper “ Equivalence existence best proximity points and pairs for cyclic noncyclic nonexpansive mappings ,” Demonstr. Math. 53 (2020), 38–43.