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 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 Random fixed point theorems for nonexpansive and contractive-type random operators on Banach spaces

1994 ◽  
Vol 7 (4) ◽  
pp. 569-580 ◽  
Author(s):  
Ismat Beg ◽  
Naseer Shahzad
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorems ◽  
Coincidence Point ◽  
Random Operators ◽  
Random Coincidence ◽  
Random Fixed Point ◽  
Random Fixed Points ◽  
Multivalued Operators ◽  
Contractive Type

The existence of random fixed points. for nonexpansive and pseudocontractive random multivalued operators defined on unbounded subsets of a Banach space is proved. A random coincidence point theorem for a pair of compatible random multivalued operators is established.

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 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 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 Random fixed points of weakly inward operators in conical shells

1995 ◽  
Vol 8 (3) ◽  
pp. 261-264 ◽  
Author(s):  
Ismat Beg ◽  
Naseer Shahzad
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Fixed Point Theorems ◽  
Random Operators ◽  
Random Fixed Point ◽  
Conical Shells ◽  
Random Fixed Points ◽  
Weakly Inward

Conditions for random fixed points of condensing random operators are obtained and subsequently used to prove random fixed point theorems for weakly inward operators in conical shells.

scholarly journals Random fixed points of non-self maps and random approximations

1997 ◽  
Vol 10 (2) ◽  
pp. 127-130 ◽  
Author(s):  
Ismat Beg
Keyword(s):  
Fixed Point ◽  
Fixed Points ◽  
Banach Spaces ◽  
Fixed Point Theorems ◽  
Approximation Theorem ◽  
Random Operators ◽  
Reflexive Banach Spaces ◽  
Random Fixed Point ◽  
Random Fixed Points

In this paper we prove random fixed point theorems in reflexive Banach spaces for nonexpansive random operators satisfying inward or Leray-Schauder condition and establish a random approximation theorem.

Random iterative algorithms and almost sure stability in Banach spaces

Filomat ◽  
2017 ◽  
Vol 31 (12) ◽  
pp. 3611-3626 ◽  
Author(s):  
Abdul Khan ◽  
Vivek Kumar ◽  
Satish Narwal ◽  
Renu Chugh
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Iterative Algorithms ◽  
Random Operator ◽  
Almost Sure Stability ◽  
Random Fixed Point ◽  
Stochastic Version ◽  
Contractive Type ◽  
Bochner Integrability ◽  
Weakly Contractive

Many popular iterative algorithms have been used to approximate fixed point of contractive type operators. We define the concept of generalized ?-weakly contractive random operator T on a separable Banach space and establish Bochner integrability of random fixed point and almost sure stability of T with respect to several random Kirk type algorithms. Examples are included to support new results and show their validity. Our work generalizes, improves and provides stochastic version of several earlier results by a number of researchers.

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