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.

scholarly journals A common unique fixed point theorem for two random operators in Hilbert spaces

2002 ◽  
Vol 32 (3) ◽  
pp. 177-182 ◽  
Author(s):  
Binayak S. Choudhury
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Hilbert Spaces ◽  
Closed Subset ◽  
Separable Hilbert Space ◽  
Unique Fixed Point ◽  
Random Operators ◽  
Nonempty Closed Subset ◽  
Random Fixed Point

We construct a sequence of measurable functions and consider its convergence to the unique common random fixed point of two random operators defined on a nonempty closed subset of a separable Hilbert space. The corresponding result in the nonrandom case is also obtained.

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 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.

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.

scholarly journals Convergence Theorems for Fixed Points of Multivalued Strictly Pseudocontractive Mappings in Hilbert Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
C. E. Chidume ◽  
C. O. Chidume ◽  
N. Djitté ◽  
M. S. Minjibir
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Hilbert Spaces ◽  
Convex Subset ◽  
Real Hilbert Space ◽  
Convergence Theorems ◽  
Strictly Pseudocontractive Mapping ◽  
Pseudocontractive Mappings ◽  
Iteration Sequence ◽  
Strictly Pseudocontractive Mappings

LetKbe a nonempty, closed, and convex subset of a real Hilbert spaceH. Suppose thatT:K→2Kis a multivalued strictly pseudocontractive mapping such thatF(T)≠∅. A Krasnoselskii-type iteration sequence{xn}is constructed and shown to be an approximate fixed point sequence ofT; that is,limn→∞d(xn,Txn)=0holds. Convergence theorems are also proved under appropriate additional conditions.

scholarly journals Parallel and Cyclic Algorithms for Quasi-Nonexpansives in Hilbert Space

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Bin-Chao Deng ◽  
Tong Chen ◽  
Baogui Xin
Keyword(s):  
Hilbert Space ◽  
Fixed Point ◽  
Strong Convergence ◽  
Common Fixed Point ◽  
Convex Subset ◽  
Real Hilbert Space ◽  
Nonexpansive Mappings

Let{T}i=1NbeNquasi-nonexpansive mappings defined on a closed convex subsetCof a real Hilbert spaceH. Consider the problem of finding a common fixed point of these mappings and introduce the parallel and cyclic algorithms for solving this problem. We will prove the strong convergence of these algorithms.

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].

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