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Approximation of *-nonexpansive random multivalued operators on Banach spaces

Part of: Nonlinear operators and their properties Approximations and expansions Stochastic analysis

Published online by Cambridge University Press:  09 April 2009

Ismat Beg ,
A. R. Khan  and
N. Hussain
Ismat Beg
Affiliation:
Lahore University of Management Sciences, Lahore, Pakistan, e-mail: ibeg@lums.edu.pk
A. R. Khan
Affiliation:
KFUPM Dhahran, Saudi Arabia
N. Hussain
Affiliation:
Bhauddin Zakariya UniversityMultan, Pakistan
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Abstract

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We establish the existence and approximation of solutions to the operator inclusion y ∈ Ty for deterministic and random cases for a nonexpansive and *-nonexpansive multivalued mapping T defined on a closed bounded (not necessarily convex) subset C of a Banach space. We also prover random fixed points and approximation results for*-nonexpansive random operators defined on an unbounded subject C of a uniformly convex Banach space.

Keywords

random fixed point*-nonexpansive random multivalued mapweakly inward orperatorLeray-Schuder conditionOpial conditionrandom approximationBanach space

MSC classification

Secondary: 47H40: Random operators 47H10: Fixed-point theorems 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) 47H09: Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc. 60H25: Random operators and equations
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 1 , February 2004 , pp. 51 - 66
Copyright
Copyright © Australian Mathematical Society 2004

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