Convergence theorems for common fixed points for finite families of nonexpansive mappings in reflexive Banach spaces

2008 ◽  
Vol 68 (11) ◽  
pp. 3410-3418 ◽  
Author(s):  
C.E. Chidume ◽  
Bashir Ali
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Reflexive Banach Spaces ◽  
Convergence Theorems

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 Approximating common fixed points of two asymptotically quasi-nonexpansive mappings in Banach spaces

2010 ◽  
Vol 42 (1) ◽  
pp. 19-30
Author(s):  
Isa Yildirim ◽  
Murat Özdemir
Keyword(s):  
Weak Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Uniformly Convex Banach Spaces

In this paper, we consider a composite iterative algorithm for approximating common fixed points of two nonself asymptotically quasi-nonexpansive mappings and we prove some strong and weak convergence theorems for such mappings in uniformly convex Banach spaces.

scholarly journals On Asymptotically Quasi-ϕ-Nonexpansive Mappings in the Intermediate Sense

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Xiaolong Qin ◽  
Lin Wang
Keyword(s):  
Strong Convergence ◽  
Fixed Points ◽  
Banach Spaces ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Convergence Theorems

A projection iterative process is investigated for the class of asymptotically quasi-ϕ-nonexpansive mappings in the intermediate sense. Strong convergence theorems of common fixed points of a family of asymptotically quasi-ϕ-nonexpansive mappings in the intermediate sense are established in the framework of Banach spaces.

Some convergence theorems for total asymptotically nonexpansive mappings in Banach spaces

2013 ◽  
Vol 63 (5) ◽  
Author(s):  
Shih-sen Chang ◽  
H. Joseph Lee ◽  
Chi Chan
Keyword(s):  
Fixed Points ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Countable Family ◽  
Convergence Theorems ◽  
Approximation Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

AbstractThe purpose of this paper is to establish some new approximation theorems of common fixed points for a countable family of total asymptotically quasi-nonexpansive mappings in Banach spaces which generalize and improve the corresponding theorems of Chidume et al. [J. Math. Anal. Appl. 333 (2007), 128–141], [J. Math. Anal. Appl. 326 (2007), 960–973], [Internat. J. Math. Math. Sci. 2009, Article ID 615107, 17 pp.] and others.

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].

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.

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