scholarly journals Convergence of a General Composite Iterative Method for a Countable Family of Nonexpansive Mappings

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Shuang Wang
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Countable Family

We propose a general composite iterative method for computing common fixed points of a countable family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and complement the corresponding ones announced by many others.

scholarly journals Some Convergence Results for a Class of Generalized Nonexpansive Mappings in Banach Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Thabet Abdeljawad ◽  
Kifayat Ullah ◽  
Junaid Ahmad ◽  
Manuel de la Sen ◽  
Muhammad Naveed Khan
Keyword(s):  
Weak Convergence ◽  
Iterative Method ◽  
Fixed Points ◽  
Banach Spaces ◽  
Current Literature ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Strong And Weak Convergence ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces

This paper investigates fixed points of Reich-Suzuki-type nonexpansive mappings in the context of uniformly convex Banach spaces through an M ∗ iterative method. Under some appropriate situations, some strong and weak convergence theorems are established. To support our results, a new example of Reich-Suzuki-type nonexpansive mappings is presented which exceeds the class of Suzuki-type nonexpansive mappings. The presented results extend some recently announced results of current literature.

An Iterative Method for Mixed Equilibrium Problems and Fixed Points

2012 ◽  
Vol 263-266 ◽  
pp. 283-286 ◽  
Author(s):  
Qiao Hong Jiang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Engineering Calculation ◽  
Common Element ◽  
Rounding Errors ◽  
Mixed Equilibrium Problems ◽  
Mixed Equilibrium

Fixed point computation plays an important role in the field of engineering calculation. Rounding errors often cause no convergence for iteration sequence or results distortion in many fixed point iterative method. In this paper, we prove the strong convergence of an iterative method for finding a common element of the set of olutions of mixed equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings under some suitable conditions. Result presented in this paper improves and extends the recent known results in this area.

An Iterative Method for Equilibrium Problems and Fixed Point Problems

2014 ◽  
Vol 513-517 ◽  
pp. 382-385
Author(s):  
Chen Min ◽  
Qiao Hong Jiang
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Fixed Point Problems ◽  
Common Element ◽  
Mixed Equilibrium Problems

In this paper, we prove the strong convergence of an iterative method for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of a finite family of nonexpansive mappings under some suitable conditions. Result presented in this paper improves and extends the recent known results in this area.

scholarly journals Coupled fixed points and α-dense curves

2016 ◽  
Vol 32 (3) ◽  
pp. 323-330
Author(s):  
G. GARCIA ◽  
Keyword(s):  
Iterative Method ◽  
Fixed Points ◽  
Integral Equations ◽  
Nonexpansive Mappings ◽  
Volterra Type ◽  
System Of Integral Equations ◽  
Compactness Condition ◽  
New Iterative Method ◽  
Coupled Fixed Points

We present a new iterative method, based on the so called α-dense curves, to approximate coupled fixed points of nonexpansive mappings. Compactness condition on the mapping or its domain of definition is necessary. As application, we construct a sequence which converges to a solution of certain system of integral equations of Volterra type.

scholarly journals Approximation of the Fixed Point of Multivalued Quasi-Nonexpansive Mappings via a Faster Iterative Process with Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11 ◽  
Author(s):  
Godwin Amechi Okeke ◽  
Mujahid Abbas ◽  
Manuel de la Sen
Keyword(s):  
Fixed Point ◽  
Iterative Method ◽  
Fixed Points ◽  
Boundary Value Problems ◽  
Rate Of Convergence ◽  
Iterative Process ◽  
Numerical Experiments ◽  
Nonexpansive Mappings ◽  
Point Boundary ◽  
Fixed Point Iterative Method

In this paper, we approximate the fixed points of multivalued quasi-nonexpansive mappings via a faster iterative process and propose a faster fixed-point iterative method for finding the solution of two-point boundary value problems. We prove analytically and with series of numerical experiments that the Picard–Ishikawa hybrid iterative process has the same rate of convergence as the CR iterative process.

scholarly journals Fixed points of quasi-nonexpansive mappings

1972 ◽  
Vol 13 (2) ◽  
pp. 167-170 ◽  
Author(s):  
W. G. Dotson
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Linear Space ◽  
Complex Plane ◽  
Normed Linear Space ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
The Other ◽  
Commuting Mappings ◽  
Analytic Mappings

A self-mapping T of a subset C of a normed linear space is said to be non-expansive provided ║Tx — Ty║ ≦ ║x – y║ holds for all x, y ∈ C. There has been a number of recent results on common fixed points of commutative families of nonexpansive mappings in Banach spaces, for example see DeMarr [6], Browder [3], and Belluce and Kirk [1], [2]. There have also been several recent results concerning common fixed points of two commuting mappings, one of which satisfies some condition like nonexpansiveness while the other is only continuous, for example see DeMarr [5], Jungck [8], Singh [11], [12], and Cano [4]. These results, with the exception of Cano's, have been confined to mappings from the reals to the reals. Some recent results on common fixed points of commuting analytic mappings in the complex plane have also been obtained, for example see Singh [13] and Shields [10].

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