A new composite implicit iterative algorithm for nonself asymptotically nonexpansive mappings

2008 ◽  
Vol 31 (1-2) ◽  
pp. 81-95
Author(s):  
Liping Yang ◽  
Xiangsheng Xie ◽  
Shiguo Peng
Keyword(s):  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Implicit Iterative Algorithm

Iterative algorithm for a split equilibrium problem and fixed problem for finite asymptotically nonexpansive mappings in Hlbert space

Filomat ◽  
2017 ◽  
Vol 31 (5) ◽  
pp. 1423-1434 ◽  
Author(s):  
Sheng Wang ◽  
Min Chen
Keyword(s):  
Equilibrium Problem ◽  
Iterative Algorithm ◽  
Nonexpansive Mappings ◽  
Common Element ◽  
Fixed Point Set ◽  
Split Equilibrium Problem ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Point Set ◽  
The Common

In this paper, we propose an iterative algorithm for finding the common element of solution set of a split equilibrium problem and common fixed point set of a finite family of asymptotically nonexpansive mappings in Hilbert space. The strong convergence of this algorithm is proved.

scholarly journals Iterative Algorithm andΔ-Convergence Theorems for Total Asymptotically Nonexpansive Mappings in CAT(0) Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-11
Author(s):  
J. F. Tang ◽  
S. S. Chang ◽  
H. W. Joseph Lee ◽  
C. K. Chan
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Algorithm ◽  
Convergence Theorem ◽  
Nonexpansive Mappings ◽  
Convergence Theorems ◽  
Demiclosed Principle ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

The main purpose of this paper is first to introduce the concept of total asymptotically nonexpansive mappings and to prove aΔ-convergence theorem for finding a common fixed point of the total asymptotically nonexpansive mappings and the asymptotically nonexpansive mappings. The demiclosed principle for this kind of mappings in CAT(0) space is also proved in the paper. Our results extend and improve many results in the literature.

Three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in uniformly convex metric spaces

Filomat ◽  
2017 ◽  
Vol 31 (11) ◽  
pp. 3573-3583
Author(s):  
Hafiz Fukhar-ud-dina ◽  
Safeer Khan
Keyword(s):  
Iterative Algorithm ◽  
Metric Spaces ◽  
Nonexpansive Mappings ◽  
Iterative Algorithms ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Convex Metric Spaces ◽  
Asymptotically Nonexpansive ◽  
Special Cases ◽  
Total Asymptotically Nonexpansive Mappings

We introduce and study a three-step iterative algorithm for a pair of total asymptotically nonexpansive mappings in a uniformly convex metric space. The proposed algorithm includes Mann and Ishikawa iterative algorithms, the iterative algorithm of Khan and Takahashi [13] and the three-step iterative algorithm of Xu and Noor [26] as special cases. Our results are new and generalize several recent results in Hilbert spaces, uniformly convex Banach spaces and CAT (0) spaces, simultaneously.

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