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.

VISCOSITY APPROXIMATION METHODS OF RANDOM FIXED POINT SOLUTIONS AND RANDOM VARIATIONAL INEQUALITIES IN HILBERT SPACES

2011 ◽  
Vol 04 (02) ◽  
pp. 283-293 ◽  
Author(s):  
Poom Kumam ◽  
Somyot Plubtieng
Keyword(s):  
Fixed Point ◽  
Variational Inequalities ◽  
Random Operators ◽  
Random Fixed Point ◽  
Stochastic Version ◽  
Iterative Processes ◽  
Random Fixed Points ◽  
Inequality Theory ◽  
Viscosity Approximation Methods ◽  
Random Variational Inequalities

In this paper, we construct random iterative processes for nonexpansive random operators and study necessary conditions for these processes. It is shown that these random iterative processes converge to random fixed points of nonexpansive random operators and solve some random variational inequalities. We also proved that an implicit random iterative process converges to the random fixed point and solves these random variational inequalities. Our results can be viewed as a refinement and improvement of the previously known results for variational inequality theory and also give generalization stochastic version of some results of Xu [23].

scholarly journals Equivalence and stability of random fixed point iterative procedures

2006 ◽  
Vol 2006 ◽  
pp. 1-19 ◽  
Author(s):  
Ismat Beg ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Hilbert Spaces ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
Random Operator ◽  
Random Operators ◽  
Random Fixed Point ◽  
The Stability ◽  
Iterative Procedures ◽  
Measurable Mappings

We generate a sequence of measurable mappings iteratively and study necessary conditions for its strong convergence to a random fixed point of strongly pseudocontractive random operator. We establish the weak convergence of an implicit random iterative procedure to common random fixed point of a finite family of nonexpansive random operators in Hilbert spaces. We prove the equivalence between the convergence of random Ishikawa and random Mann iterative schemes for contraction random operator and strongly pseudocontractive random operator. We also examine the stability of random fixed point iterative procedures for the random operators satisfying certain contractive conditions in the context of metric spaces.

Random fixed points of asymptotically nonexpansive random operators on unbounded domains

2008 ◽  
Vol 58 (6) ◽  
Author(s):  
Ismat Beg ◽  
Mujahid Abbas
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Unbounded Domains ◽  
Random Operator ◽  
Random Operators ◽  
Random Fixed Point ◽  
Random Fixed Points ◽  
Asymptotically Nonexpansive

AbstractThe aim of this paper is to prove some random fixed point theorems for asymptotically nonexpansive random operator defined on an unbounded closed and starshaped subset of a Banach space.

scholarly journals Convergence of a random iteration scheme to a random fixed point

1995 ◽  
Vol 8 (2) ◽  
pp. 139-142 ◽  
Author(s):  
Binayak S. Choudhury
Keyword(s):  
Fixed Point ◽  
Iteration Scheme ◽  
Random Operators ◽  
Random Fixed Point ◽  
Ishikawa Iteration ◽  
Random Iteration

This paper discusses the convergence of random Ishikawa iteration scheme to a random fixed point for a certain class of random operators.

scholarly journals Common random fixed points of compatible random operators

2006 ◽  
Vol 2006 ◽  
pp. 1-15 ◽  
Author(s):  
Ismat Beg ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Symmetric Spaces ◽  
Fixed Point Theorems ◽  
Iteration Scheme ◽  
Random Operators ◽  
Random Fixed Point ◽  
Polish Spaces ◽  
Random Fixed Points ◽  
Weakly Compatible ◽  
Random Iteration

We construct a random iteration scheme and study necessary conditions for its convergence to a common random fixed point of two pairs of compatible random operators satisfying Meir-Keeler type conditions in Polish spaces. Some random fixed point theorems for weakly compatible random operators under generalized contractive conditions in the framework of symmetric spaces are also proved.

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 Convergence of iterative algorithms to common random fixed points of random operators

2006 ◽  
Vol 2006 ◽  
pp. 1-16 ◽  
Author(s):  
Ismat Beg ◽  
Mujahid Abbas
Keyword(s):  
Fixed Point ◽  
Iterative Algorithms ◽  
Random Operators ◽  
Uniformly Convex ◽  
Necessary And Sufficient Condition ◽  
Random Fixed Point ◽  
Random Fixed Points ◽  
Uniformly Convex Banach Spaces ◽  
Asymptotically Nonexpansive ◽  
Necessary And Sufficient

We prove the existence of a common random fixed point of two asymptotically nonexpansive random operators through strong and weak convergences of an iterative process. The necessary and sufficient condition for the convergence of sequence of measurable functions to a random fixed point of asymptotically quasi-nonexpansive random operators in uniformly convex Banach spaces is also established.

scholarly journals An iteration for finding a common random fixed point

2004 ◽  
Vol 2004 (4) ◽  
pp. 385-394
Author(s):  
Binayak S. Choudhury
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Convex Subset ◽  
Separable Hilbert Space ◽  
Iteration Scheme ◽  
Random Operators ◽  
Random Fixed Point ◽  
Random Iteration

We define a random iteration scheme and consider its convergence to a common random fixed point of two random operators defined on a convex subset of a separable Hilbert space. We also consider the case when the subset is further compact.

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