Some random fixed point theorems for random asymptotically regular operators

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

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Publication Details

Author list: Kumam P., Plubtieng S.

Publisher: Warsaw University

Publication year: 2009

Journal: Demonstratio Mathematica- Politechnika Warszawska (0420-1213)

Volume number: 42

Issue number: 1

Start page: 131

End page: 141

Number of pages: 11

ISSN: 0420-1213

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84902498268&partnerID=40&md5=777e121780f32aa1433352242e3a2726

Languages: English-Great Britain (EN-GB)

Abstract

Let (Ω, ∑) be a measurable space, X a Banach space, C a weakly compact convex subset of X and T : Ω × C -→ C a random operator. Let WCS(X) be the weakly convergent sequence coefficient of X and κω its Lifschitz characteristic. If T is asymptotically regular and assume that there exists ω ∈ Ωand constant c such that, σ(T(ω, ))≤ c< 1+√1+4WCS(X) (κω(X) -1we prove that T has a random fixed point. © 2009 Warsaw University. All rights reserved.

Keywords

Lifschititz characteristic, Random asymptotically regular, Uniformly lipschitzian mapping