scholarly journals Some Theorems of Fixed Point Approximations By Iteration Processes

2021 ◽  
Vol 1818 (1) ◽  
pp. 012153
Author(s):  
Z. H. Maibed ◽  
S. S. Hussein
Keyword(s):  
Fixed Point ◽  
Iteration Processes

scholarly journals Implicit Ishikawa Approximation Methods for Nonexpansive Semigroups in CAT(0) Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhi-bin Liu ◽  
Yi-shen Chen ◽  
Xue-song Li ◽  
Yi-bin Xiao
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Nonexpansive Mappings ◽  
Nonexpansive Semigroup ◽  
Approximation Methods ◽  
Ishikawa Iteration ◽  
Nonexpansive Semigroups ◽  
Convergence Results ◽  
Iteration Processes

This paper is devoted to the convergence of the implicit Ishikawa iteration processes for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain theΔ-convergence results of the implicit Ishikawa iteration sequences for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Ishikawa iteration sequences for nonexpansive semigroups in the CAT(0) spaces. The results presented in this paper extend and generalize some previous results.

scholarly journals Mann Iteration Processes on Uniform Convex n-Banach Space

2019 ◽  
pp. 1063-1608
Author(s):  
Mustafa Mohamed Hamed ◽  
Zeana Zaki Jamil
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Convex Subset ◽  
Convex Set ◽  
Nonempty Closed Convex Subset ◽  
Nonlinear Mapping ◽  
Uniformly Convex ◽  
Mann Iteration ◽  
Iteration Processes

Let Y be a"uniformly convex n-Banach space, M be a nonempty closed convex subset of Y, and S:M→M be adnonexpansive mapping. The purpose of this paper is to study some properties of uniform convex set that help us to develop iteration techniques for1approximationjof"fixed point of nonlinear mapping by using the Mann iteration processes in n-Banachlspace.

scholarly journals Fixed-point iteration processes for non-Lipschitzian mappings of asymptotically quasi-nonexpansive type

2003 ◽  
Vol 2003 (33) ◽  
pp. 2075-2081 ◽  
Author(s):  
Daya Ram Sahu ◽  
Jong Soo Jung
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Fixed Point Iteration ◽  
Ishikawa Iteration ◽  
Lipschitzian Mappings ◽  
Iteration Processes

We study convergences of Mann and Ishikawa iteration processes for mappings of asymptotically quasi-nonexpansive type in Banach spaces.

scholarly journals Iterative processes with errors for nonlinear equations

2004 ◽  
Vol 69 (2) ◽  
pp. 177-189 ◽  
Author(s):  
Łjubomir Ćirić ◽  
Jeong Sheok Ume
Keyword(s):  
Fixed Point ◽  
Nonlinear Equations ◽  
Unique Fixed Point ◽  
Convergence Theorems ◽  
Mann Iteration ◽  
General Lemma ◽  
Iterative Processes ◽  
Iteration Processes ◽  
Lipschitz Operators ◽  
Monotone Type

In this paper we introduce and consider a class of multi-valued and single-valued operators of generalised monotone type. We proved a new general lemma on the convergence of real sequences and some new convergence theorems for the Ishikawa and Mann iteration processes with errors to the unique fixed point of such operators, which are not necessarily Lipschitz operators. Our results generalise, improve, and extend several recent results.

scholarly journals A new iteration scheme for approximating fixed points of nonexpansive mappings

Filomat ◽  
2016 ◽  
Vol 30 (10) ◽  
pp. 2711-2720 ◽  
Author(s):  
Balwant Thakur ◽  
Dipti Thakur ◽  
Mihai Postolache
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Iteration Process ◽  
Iteration Scheme ◽  
Numerical Example ◽  
Convergence Results ◽  
Iteration Processes

In this paper, we introduce a new three-step iteration scheme and establish convergence results for approximation of fixed points of nonexpansive mappings in the framework of Banach space. Further, we show that the new iteration process is faster than a number of existing iteration processes. To support the claim, we consider a numerical example and approximated the fixed point numerically by computer using MATLAB.

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