Weak Convergence Theorems for Mixed Type Total Asymptotically Nonexpansive Mappings in Uniformly Convex Banach Spaces

2017 ◽  
Vol 50 (4) ◽  
pp. 375-390
Author(s):  
Gurucharan Singh Saluja
Keyword(s):  
Weak Convergence ◽  
Banach Spaces ◽  
Mixed Type ◽  
Nonexpansive Mappings ◽  
Uniformly Convex ◽  
Convergence Theorems ◽  
Asymptotically Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings

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.

Strong and weak convergence theorems for fixed points of a class of nonlinear mappings

2014 ◽  
Vol 64 (2) ◽  
Author(s):  
Changqun Wu ◽  
Zhiqiang Wei ◽  
Yu Li
Keyword(s):  
Weak Convergence ◽  
Hilbert Spaces ◽  
Nonexpansive Mappings ◽  
Projection Methods ◽  
Convergence Theorems ◽  
Strong And Weak Convergence ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Total Asymptotically Nonexpansive Mappings ◽  
Weak Convergence Theorem

AbstractIn this paper, the class of total asymptotically nonexpansive mappings is considered. A weak convergence theorem of Mann-type iterative algorithm is established. Hybrid projection methods are considered for the class of total asymptotically nonexpansive mappings. Strong convergence theorems are also established in the framework of Hilbert spaces.

Approximating common fixed point of asymptotically nonexpansive mappings without convergence condition

2017 ◽  
Vol 33 (3) ◽  
pp. 327-334
Author(s):  
ABDUL RAHIM KHAN ◽  
◽  
HAFIZ FUKHAR-UD-DIN ◽  
NUSRAT YASMIN ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Convergence Condition ◽  
Finite Family ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive

In the context of a hyperbolic space, we introduce and study convergence of an implicit iterative scheme of a finite family of asymptotically nonexpansive mappings without convergence condition. The results presented substantially improve and extend several well-known resullts in uniformly convex Banach spaces.

scholarly journals Convergence of a Three-step Iteration Scheme to the Common Fixed Points of Mixed-Type Total Asymtotically Nonexpansive Mappings in Uniformly Convex Banach Spaces

2021 ◽  
Vol 1 (1) ◽  
pp. 45-67
Author(s):  
Imo Kalu Agwu ◽  
Donatus Ikechi Igbokwe ◽  
Nathenial C. Ukeje
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Mixed Type ◽  
Nonexpansive Mappings ◽  
Common Fixed Points ◽  
Iteration Scheme ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive ◽  
The Common

We propose a three-step iteration scheme of hybrid mixed-type for three total asymptotically nonexpansive self mappings and three total asymptotically nonexpansive nonself mappings. In addition, we establish some weak convergence theorems of the scheme to the common fixed point of the mappings in uniformly convex Banach spaces. Our results extend and generalize numerous results currently in literature.

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.

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