Set-valued nonlinear contractive operators in $PM$-spaces

Document Type : Research Paper

Authors

1 Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.

2 Department of Mathematics, Shahid Chamran University, of Ahvaz, Ahvaz, Iran

3 Faculty of Fundamental Science, Industrial University of Ho Chi Minh City, Ho Chi Minh, Vietnam, Department of Mathematics, C¸ankaya University, 06790, Etimesgut, Ankara, Turkey

4 Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, P. O. Box 13185/768, Tehran, Iran &amp;amp; Young Researchers and Elite club, Central Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

In this paper, we consider some nonlinear contraction for set-valued operators and prove some fixed point results in the case of set-valued operators are ordered-close and not ordered-close, and in the case of set-valued operators are UCAV (LCAV) in quasi-ordered $PM$-spaces. Moreover, we present two examples and an application to show the validity of the main theorems.

Keywords