scholarly journals Hybrid Algorithms of Nonexpansive Semigroups for Variational Inequalities

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Peixia Yang ◽  
Yonghong Yao ◽  
Yeong-Cheng Liou ◽  
Rudong Chen
Keyword(s):  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Common Fixed Points ◽  
Hybrid Algorithms ◽  
Nonexpansive Semigroups ◽  
Convergence Results ◽  
The Common ◽  
Two Hybrid

Two hybrid algorithms for the variational inequalities over the common fixed points set of nonexpansive semigroups are presented. Strong convergence results of these two hybrid algorithms have been obtained in Hilbert spaces. The results improve and extend some corresponding results in the literature.

scholarly journals Convergence of two-step iterative scheme with errors for two asymptotically nonexpansive mappings

2004 ◽  
Vol 2004 (37) ◽  
pp. 1965-1971 ◽  
Author(s):  
Hafiz Fukhar-ud-din ◽  
Safeer Hussain Khan
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Weak And Strong Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
The Common

A two-step iterative scheme with errors has been studied to approximate the common fixed points of two asymptotically nonexpansive mappings through weak and strong convergence in Banach spaces.

scholarly journals Fixed Points Approximation and Solutions of Some Equilibrium and Variational Inequalities Problems

2009 ◽  
Vol 2009 ◽  
pp. 1-17 ◽  
Author(s):  
Bashir Ali
Keyword(s):  
Variational Inequality ◽  
Variational Inequalities ◽  
Strong Convergence ◽  
Fixed Points ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Strong Convergence Theorem ◽  
Points Approximation

We prove a new strong convergence theorem for an element in the intersection of the set of common fixed points of a countable family of nonexpansive mappings, the set of solutions of some variational inequality problems, and the set of solutions of some equilibrium problems using a new iterative scheme. Our theorem generalizes and improves some recent results.

scholarly journals Common fixed points of monotone ρ-nonexpansive semigroup in modular spaces

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Noureddine El Harmouchi ◽  
Karim Chaira ◽  
El Miloudi Marhrani
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Common Fixed Point ◽  
Common Fixed Points ◽  
Nonexpansive Semigroup ◽  
Iteration Algorithm ◽  
Uniformly Convex ◽  
Modular Spaces ◽  
Nonexpansive Semigroups ◽  
Convergence Results

Abstract In this paper, we consider the class of monotone ρ-nonexpansive semigroups and give existence and convergence results for common fixed points. First, we prove that the set of common fixed points is nonempty in uniformly convex modular spaces and modular spaces. Then we introduce an iteration algorithm to approximate a common fixed point for the same class of semigroups.

scholarly journals Viscosity Method for Hierarchical Fixed Point Problems with an Infinite Family of Nonexpansive Nonself-Mappings

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Yaqin Wang
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Fixed Points ◽  
Infinite Family ◽  
Common Fixed Points ◽  
Fixed Point Problems ◽  
Viscosity Method ◽  
Hierarchical Fixed Point ◽  
The Common ◽  
Hierarchical Fixed Point Problems

A viscosity method for hierarchical fixed point problems is presented to solve variational inequalities, where the involved mappings are nonexpansive nonself-mappings. Solutions are sought in the set of the common fixed points of an infinite family of nonexpansive nonself-mappings. The results generalize and improve the recent results announced by many other authors.

scholarly journals Iterative approximations of common fixed points with simulation results in Banach spaces

2020 ◽  
Author(s):  
Ashis Bera ◽  
Ankush Chanda ◽  
Lakshmi Kanta Dey
Keyword(s):  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Iteration Scheme ◽  
The Other ◽  
The Novel ◽  
Weak And Strong Convergence ◽  
Analytic Proof ◽  
Convergence Results ◽  
The Common

In this article, we propose the Abbas-Nazir three step iteration scheme and employ the algorithm to study the common fixed points of a pair of generalized $\alpha$-Reich-Suzuki non-expansive mappings defined on a Banach space. Moreover, we explore a few weak and strong convergence results concerning such mappings. Our findings are aptly validated by non-trivial and constructive numerical examples and finally, we compare our results with that of the other noteworthy iterative schemes utilizing MATLAB $2017$a software. However, we perceive that for a different set of parameters and initial points, the newly proposed iterative scheme converges faster than the other well-known algorithms. To be specific, we give an analytic proof of the claim that the novel iteration scheme is also faster than that of Liu et al.

scholarly journals Common Fixed Points for Weak and Strong Convergence Results

2016 ◽  
Vol 4 (2) ◽  
pp. 340
Author(s):  
S. C. Shrivastava
Keyword(s):  
Banach Space ◽  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Convex Banach Space ◽  
Uniformly Convex Banach Space ◽  
Uniformly Convex ◽  
Weak And Strong Convergence ◽  
Convergence Results

<div><p> <em>In this paper, we study the approximation of common fixed points for more general classes of mappings through weak and strong convergence results of an iterative scheme in a uniformly convex Banach space. Our results extend and improve some known recent results.</em></p></div>

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