Random fixed point theorems for multivalued nonexpansive non-self-random operators

S. Plubtieng,

S. Plubtieng

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

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P. Kumam,

P. Kumam

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand

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S. Plubtieng,

S. Plubtieng

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Search for more papers by this author

P. Kumam,

P. Kumam

Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, Thailand

Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi, Bangkok 10140, Thailand

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First published: 25 April 2006

https://doi.org/10.1155/JAMSA/2006/43796

Citations: 3

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Abstract

Let (Ω, Σ) be a measurable space, with Σ a sigma-algebra of subset of Ω, and let C be a nonempty bounded closed convex separable subset of a Banach space X, whose characteristic of noncompact convexity is less than 1, KC(X) the family of all compact convex subsets of X. We prove that a multivalued nonexpansive non-self-random operator T : Ω × C → KC(X), 1-χ-contractive mapping, satisfying an inwardness condition has a random fixed point.

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