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Symmetry 2019, 11(2), 143; https://doi.org/10.3390/sym11020143

Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation

1
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
2
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
3
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
4
Department of Mathematics, Faculty of Experimental Science, University of Jaén, Campus Las Lagunillas, s/n, 23071 Jaén, Spain
5
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok (KMUTNB), Wongsawang, Bangsue, Bangkok 10800, Thailand
*
Author to whom correspondence should be addressed.
Received: 27 October 2018 / Revised: 18 January 2019 / Accepted: 18 January 2019 / Published: 28 January 2019
(This article belongs to the Special Issue Fixed Point Theory and Fractional Calculus with Applications)
Full-Text   |   PDF [759 KB, uploaded 28 January 2019]

Abstract

The main purpose in this paper is to define the modification form of random α -admissible and random α - ψ -contractive maps. We establish new random fixed point theorems in complete separable metric spaces. The interpretation of our results provide the main theorems of Tchier and Vetro (2017) as directed corollaries. In addition, some applications to second order random differential equations are presenred here to interpret the usability of the obtained results. View Full-Text
Keywords: random fixed point; random α-admissible with respect to η; generalized random α-ψ-contractive mapping random fixed point; random α-admissible with respect to η; generalized random α-ψ-contractive mapping
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Kongban, C.; Kumam, P.; Martínez-Moreno, J.; Sitthithakerngkiet, K. Generalized Random α-ψ-Contractive Mappings with Applications to Stochastic Differential Equation. Symmetry 2019, 11, 143.

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