scholarly journals Approximation of common random fixed point for a finite family of non-self asymptotically nonexpansive random mappings

2009 ◽  
Vol 42 (3) ◽  
Author(s):  
G. S. Saluja
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iteration Scheme ◽  
Finite Family ◽  
Uniformly Convex ◽  
Random Fixed Point ◽  
Asymptotically Nonexpansive ◽  
Random Iteration ◽  
Random Mappings

AbstractIn this paper, we study multi-step random iteration scheme with errors for a common random fixed point of a finite family of nonself asymptotically nonexpansive random mappings in real uniformly convex separable Banach spaces. The results presented in this paper extend the recent ones announced by Zhou and Wang [

scholarly journals Approximation of a Common Random Fixed Point for a Finite Family of Random Operators

2007 ◽  
Vol 2007 ◽  
pp. 1-12 ◽  
Author(s):  
Somyot Plubtieng ◽  
Poom Kumam ◽  
Rabian Wangkeeree
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Iteration Process ◽  
Finite Family ◽  
Random Operators ◽  
Uniformly Convex ◽  
Random Fixed Point ◽  
Uniformly Convex Banach Spaces ◽  
Random Iteration

We construct implicit random iteration process with errors for a common random fixed point of a finite family of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces. The results presented in this paper extend and improve the corresponding results of Beg and Abbas in 2006 and many others.

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 Common fixed point iterations for a class of multi-valued mappings in $$\mathbf {CAT}(0)$$ spaces

2020 ◽  
Vol 9 (3) ◽  
pp. 681-690
Author(s):  
Khairul Saleh ◽  
Hafiz Fukhar-ud-din
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Iterative Scheme ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Uniformly Convex ◽  
Uniformly Convex Banach Spaces ◽  
Fixed Point Iterations

Abstract In this work, we propose an iterative scheme to approach common fixed point(s) of a finite family of generalized multi-valued nonexpansive mappings in a CAT(0) space. We establish and prove convergence theorems for the algorithm. The results are new and interesting in the theory of $$CAT\left( 0\right) $$ C A T 0 spaces and are the analogues of corresponding ones in uniformly convex Banach spaces and Hilbert spaces.

scholarly journals Convergence theorems of the sequence of iterates for a finite family asymptotically nonexpansive mappings

2001 ◽  
Vol 27 (11) ◽  
pp. 653-662 ◽  
Author(s):  
Jui-Chi Huang
Keyword(s):  
Banach Space ◽  
Nonexpansive Mappings ◽  
Iteration Scheme ◽  
Nonempty Closed Convex Subset ◽  
Convex Banach Space ◽  
Finite Family ◽  
Uniformly Convex ◽  
Asymptotically Nonexpansive Mappings ◽  
Asymptotically Nonexpansive ◽  
Bounded Sequences

LetEbe a uniformly convex Banach space,Ca nonempty closed convex subset ofE. In this paper, we introduce an iteration scheme with errors in the sense of Xu (1998) generated by{Tj:C→C}j=1ras follows:Un(j)=an(j)I+bn(j)TjnUn(j−1)+cn(j)un(j),j=1,2,…,r,x1∈C,xn+1=an(r)xn+bn(r)TrnUn(r−1)xn+cn(r)un(r),n≥1, whereUn(0):=I,Ithe identity map; and{un(j)}are bounded sequences inC; and{an(j)},{bn(j)}, and{cn(j)}are suitable sequences in[0,1]. We first consider the behaviour of iteration scheme above for a finite family of asymptotically nonexpansive mappings. Then we generalize theorems of Schu and Rhoades.

scholarly journals Convergence of Common Random Fixed Point of Finite Family of Asymptotically Quasi-Nonexpansive-Type Mappings by an Implicit Random Iterative Scheme

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
A. S. Saluja ◽  
Pankaj kumar Jhade
Keyword(s):  
Banach Space ◽  
Iterative Scheme ◽  
Sufficient Conditions ◽  
Iteration Process ◽  
Convex Banach Space ◽  
Finite Family ◽  
Uniformly Convex ◽  
Random Fixed Point ◽  
Random Iteration ◽  
Necessary And Sufficient

We introduce a new implicit random iteration process generated by a finite family of asymptotically quasi-nonexpansive-type mappings and study necessary and sufficient conditions for the convergence of this process in a uniformly convex Banach space. The results presented in this paper extend and improve the recent ones announced by Plubtieng et al. (2007), Beg and Thakur (2009), and Saluja and Nashine (2012).

scholarly journals Random Three-Step Iteration Scheme and Common Random Fixed Point of Three Operators

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Somyot Plubtieng ◽  
Poom Kumam ◽  
Rabian Wangkeeree
Keyword(s):  
Fixed Point ◽  
Necessary Conditions ◽  
Iteration Scheme ◽  
Random Operators ◽  
Random Fixed Point ◽  
Iterative Processes ◽  
Asymptotically Nonexpansive

We construct random iterative processes with errors for three asymptotically nonexpansive random operators and study necessary conditions for the convergence of these processes. The results presented in this paper extend and improve the recent ones announced by I. Beg and M. Abbas (2006), and many others.

Sign in / Sign up

Export Citation Format

Share Document