Stochastic fixed point theorems for a random Z-contraction in a complete probability measure space with application to non-linear stochastic integral equations

Volume 1, Issue 1, pp 40--48

Publication Date: 2017-11-01

http://dx.doi.org/10.22436/mns.01.01.05

Authors

Plern Saipara - KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Poom Kumam - KMUTT-Fixed Point Theory and Applications Research Group (KMUTT-FPTA), Theoretical and Computational Science Center (TaCS), Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Apirak Sombat - KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Anantachai Padcharoen - KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand
Wiyada Kumam - Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi, Thanyaburi (RMUTT), Pathumthani 12110, Thailand

Abstract

In this paper, we propose the random \(\mathcal{Z}\)-contraction, prove a stochastic fixed point theorem for this contraction, and show that a solution for a non-linear stochastic integral equations exists in Banach spaces.

Keywords

\(\mathcal{Z}\)-contraction, stochastic fixed point theorem, complete probability measure spaces

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