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Random Operators and Stochastic Equations

Editor-in-Chief: Girko, Vyacheslav

Managing Editor: Molchanov, S.

Editorial Board: Accardi, L. / Albeverio, Sergio / Carmona, R. / Casati, G. / Christopeit, N. / Domanski, C. / Drygas, Hilmar / Gupta, A.K. / Ibragimov, I. / Kirsch, Werner / Klein, A. / Kondratyev, Yuri / Kurotschka, V. / Leonenko, N. / Loubaton, Philippe / Orsingher, E. / Pastur, L. / Rodrigues, Waldyr A. / Shiryaev, Albert / Turbin, A.F. / Veretennikov, Alexandre

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Volume 24, Issue 2

Issues

Random fixed point theorem in generalized Banach space and applications

Moulay Larbi Sinacer / Juan Jose Nieto
  • Departamento de Análisis Matemático, Facultad de Matemáticas Universidad de Santiago de Compostela, Santiago de Compostela, 15782, Spain; and Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, 21589, Jeddah, Saudi Arabia
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/ Abdelghani Ouahab
Published Online: 2016-04-12 | DOI: https://doi.org/10.1515/rose-2016-0007

Abstract

In this paper, we prove some random fixed point theorems in generalized Banach spaces. We establish a random version of a Krasnoselskii-type fixed point theorem for the sum of a contraction random operator and a compact operator. The results are used to prove the existence of solution for random differential equations with initial and boundary conditions. Finally, some examples are given to illustrate the results.

Keywords: Multivalued map; measurable selection; generalized metric space; fixed point; random operator; random differential equation

MSC: 47H10; 47H30; 54H25

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About the article

Received: 2015-07-01

Revised: 2015-09-14

Accepted: 2016-01-14

Published Online: 2016-04-12

Published in Print: 2016-06-01


Funding Source: Ministerio de Economía y Competitividad (Spain)

Award identifier / Grant number: MTM2010-15314

Funding Source: European Commission

Award identifier / Grant number: FEDER

The research has partially been supported by Ministerio de Economía y Competitividad (Spain), project MTM2010-15314, and co-financed by the European Community fund FEDER.


Citation Information: Random Operators and Stochastic Equations, Volume 24, Issue 2, Pages 93–112, ISSN (Online) 1569-397X, ISSN (Print) 0926-6364, DOI: https://doi.org/10.1515/rose-2016-0007.

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