scholarly journals Some convergence theorems involving proximal point and common fixed points for asymptotically nonexpansive mappings in CAT ( 0 ) $\operatorname {CAT}(0)$ spaces

2016 ◽  
Vol 2016 (1) ◽  
Author(s):  
Shih-sen Chang ◽  
Jen-Chih Yao ◽  
Lin Wang ◽  
Li Juan Qin
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Proximal Point ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive

scholarly journals Common Fixed Points of Two Multivalued Asymptotically Nonexpansive Mappings

2019 ◽  
Vol 12 (2) ◽  
pp. 348-357
Author(s):  
Safeer Hussain Khan ◽  
Hira Iqbal ◽  
Mujahid Abbas
Keyword(s):  
Fixed Points ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Ishikawa Iterative Process

In this paper, we construct a modified Ishikawa iterative process to approximate common fixed points for two multivalued asymptotically nonexpansive mappings and prove some convergence theorems in uniformly convex hyperbolic 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 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 On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Farrukh Mukhamedov ◽  
Mansoor Saburov
Keyword(s):  
Strong Convergence ◽  
Banach Spaces ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Nonempty Closed Convex Subset ◽  
Finite Family ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptoticallyI-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by (C. E. Chidume and E. U. Ofoedu, 2009). We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family of total asymptoticallyI-nonexpansive and total asymptotically nonexpansive mappings, defined on a nonempty closed-convex subset of uniformly convex Banach spaces. Moreover, our results extend and unify all known results.

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