Document Type : Research Paper
Department of Mathematics, Shahid Chamran University of Ahvaz, Ahvaz, Iran.
Department of Mathematics, Shahid Chamran University, of Ahvaz, Ahvaz, Iran
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
Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, P. O. Box 13185/768, Tehran, Iran &amp; Young Researchers and Elite club, Central Tehran Branch, Islamic Azad University, Tehran, Iran
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.