scholarly journals A Modified Mixed Ishikawa Iteration for Common Fixed Points of Two Asymptotically Quasi Pseudocontractive Type Non-Self-Mappings

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Yuanheng Wang ◽  
Huimin Shi
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Iterative Scheme ◽  
Common Fixed Points ◽  
Iterative Sequence ◽  
Convergence Theorems ◽  
Ishikawa Iteration ◽  
Ishikawa Iterative Sequence

A new modified mixed Ishikawa iterative sequence with error for common fixed points of two asymptotically quasi pseudocontractive type non-self-mappings is introduced. By the flexible use of the iterative scheme and a new lemma, some strong convergence theorems are proved under suitable conditions. The results in this paper improve and generalize some existing results.

Generalized three-step iteration schemes and common fixed points of three asymptotically quasi-nonexpansive mappings

2008 ◽  
Vol 41 (4) ◽  
Author(s):  
R. A. Rashwan ◽  
A. A. Abdel Hakim
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convergence Theorems

AbstractIn this paper, we study strong convergence theorems for a generalized three-step iterative scheme with errors to approximate common fixed points of three asymptotically quasi-nonexpansive mappings in real Banach spaces. Our results generalize and improve upon the corresponding results in [

scholarly journals Common fixed points of two finite families of nonexpansive mappings by iterations

2015 ◽  
Vol 31 (3) ◽  
pp. 325-331
Author(s):  
HAFIZ FUKHAR-UD-DIN ◽  
◽  
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Uniformly Convex Banach Spaces

We study a Mann type iterative scheme for two finite families of nonexpansive mappings and establish 4− convergence and strong convergence theorems. The obtained results are applicable in uniformly convex Banach spaces (linear domain) and CAT (0) spaces (nonlinear domain) simultaneously.

scholarly journals Strong andΔ-Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT(0)Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
C. E. Chidume ◽  
A. U. Bello ◽  
P. Ndambomve
Keyword(s):  
Fixed Point ◽  
Strong Convergence ◽  
Fixed Points ◽  
Common Fixed Points ◽  
Finite Family ◽  
Iterative Sequence ◽  
Convergence Theorems ◽  
The Family ◽  
Demicontractive Mappings ◽  
Nonlinear Mappings

LetKbe a nonempty closed and convex subset of a complete CAT(0) space. LetTi:K→CBK,i=1,2,…,m, be a family of multivalued demicontractive mappings such thatF:=⋂i=1mF(Ti)≠∅. A Krasnoselskii-type iterative sequence is shown toΔ-converge to a common fixed point of the familyTi,i=1,2,…,m. Strong convergence theorems are also proved under some additional conditions. Our theorems complement and extend several recent important results on approximation of fixed points of certain nonlinear mappings in CAT(0)spaces. Furthermore, our method of the proof is of special interest.

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 Strong Convergence Theorems of Common Fixed Points for a Family of Quasi-ϕ-Nonexpansive Mappings

2010 ◽  
Vol 2010 ◽  
pp. 1-11
Author(s):  
Xiaolong Qin ◽  
Yeol Je Cho ◽  
Sun Young Cho ◽  
Shin Min Kang
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convergence Theorems

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 Strong Convergence Theorems for Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

2010 ◽  
Vol 2010 ◽  
pp. 1-13
Author(s):  
Jian-Wen Peng ◽  
Yan Wang
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Nonexpansive Mapping ◽  
Strong Convergence ◽  
Fixed Points ◽  
Hilbert Spaces ◽  
Equilibrium Problems ◽  
Iterative Scheme ◽  
Common Element ◽  
Convergence Theorems

We introduce an Ishikawa iterative scheme by the viscosity approximate method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in Hilbert space. Then, we prove some strong convergence theorems which extend and generalize S. Takahashi and W. Takahashi's results (2007).

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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