scholarly journals A one-step implicit iterative process for a finite family of I-nonexpansive mappings in Kohlenbach hyperbolic spaces

2016 ◽  
Vol 10 (1-2) ◽  
pp. 55-61 ◽  
Author(s):  
Birol Gunduz ◽  
Sezgin Akbulut
Keyword(s):  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Hyperbolic Spaces ◽  
One Step

Iteration schema for common fixed points of nonlinear mappings in spaces of nonpositive curvature

2014 ◽  
Vol 5 (2) ◽  
Author(s):  
Muhammad Aqeel Ahmad Khan
Keyword(s):  
Fixed Points ◽  
Nonexpansive Mappings ◽  
Nonpositive Curvature ◽  
Common Fixed Points ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
One Step ◽  
Uniformly Continuous ◽  
Nonlinear Mappings

Abstract.In this paper, we propose a one-step iteration for the approximation of common fixed points of two uniformly continuous total asymptotically quasi-nonexpansive mappings in uniformly convex hyperbolic spaces. We establish strong convergence and Δ-convergence results of the proposed iteration in this setting. As a consequence, our convergence results improve and generalize various results announced in the current literature.

scholarly journals Strong Convergence Theorems for a Common Fixed Point of a Finite Family of Bregman Weak Relativity Nonexpansive Mappings in Reflexive Banach Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Habtu Zegeye ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Finite Family ◽  
Important Class ◽  
Reflexive Banach Spaces ◽  
Nonlinear Operators ◽  
Relatively Nonexpansive Mappings ◽  
Relatively Nonexpansive

We introduce an iterative process for finding an element of a common fixed point of a finite family of Bregman weak relatively nonexpansive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.

scholarly journals Convergence of implicit iterates with errors for mappings with unbounded domain in Banach spaces

2005 ◽  
Vol 2005 (10) ◽  
pp. 1643-1653 ◽  
Author(s):  
Hafiz Fukhar-Ud-Din ◽  
Abdul Rahim Khan
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Unbounded Domain ◽  
Iterative Process ◽  
Error Term ◽  
Nonexpansive Mappings ◽  
Convex Banach Space ◽  
Finite Family ◽  
Iterative Sequence ◽  
Uniformly Convex

We prove that an implicit iterative process with errors converges weakly and strongly to a common fixed point of a finite family of asymptotically quasi-nonexpansive mappings on unbounded sets in a uniformly convex Banach space. Our results generalize and improve upon, among others, the corresponding recent results of Sun (2003) in the following two different directions: (i) domain of the mappings is unbounded, (ii) the iterative sequence contains an error term.

scholarly journals Fixed Point Approximation of Nonexpansive Mappings on a Nonlinear Domain

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Safeer Hussain Khan
Keyword(s):  
Fixed Point ◽  
Banach Spaces ◽  
Hyperbolic Space ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Hyperbolic Spaces ◽  
Uniformly Convex ◽  
Convergence Results ◽  
Uniformly Convex Banach Spaces ◽  
Uniformly Convex Hyperbolic Space

We use a three-step iterative process to prove some strong andΔ-convergence results for nonexpansive mappings in a uniformly convex hyperbolic space, a nonlinear domain. Three-step iterative processes have numerous applications and hyperbolic spaces contain Banach spaces (linear domains) as well as CAT(0) spaces. Thus our results can be viewed as extension and generalization of several known results in uniformly convex Banach spaces as well as CAT(0) spaces.

scholarly journals Convergence of implicit iterative process for a finite family of I-nonexpansive mappings

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
Seyit Temir ◽  
Goknur Aykanat
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Iterative Process ◽  
Nonexpansive Mappings ◽  
Finite Family

AbstractWe prove that an implicit iterative process converges weakly and strongly to a common fixed point of a finite family of

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