Generalized Z-contraction on quasi metric spaces and a fixed point result

Abstract

The simulation function is defined by Khojasteh et al. [F. Khojasteh, S. Shukla, S. Radenovic, Filomat, 29 (2015), 1189-1194]. Khojasteh introduced the notion of Z-contraction which is a new type of nonlinear contractions defined by using a specific simulation function. Then, they proved existence and uniqueness of fixed points for Z-contraction mappings. After this work, studies involving simulation functions were performed by various authors [H. H. Alsulami, E. Karapinar, F. Khojasteh, A. F. Roldan-Lopez-de-Hierro, Discrete Dyn. Nat. Soc., 2014 (2014), 10 pages], [M. Olgun, O. Bicer, T. Alyildiz, Turkish J. Math., 40 (2016), 832-837]. In this paper, we introduce generalized simulation function on a quasi metric space and we present a fixed point theorem. (C) 2017 All rights reserved.