Generalized \(\mathit{Z}\)-contraction on quasi metric spaces and a fixed point result


Authors

Hakan Şimşek - Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey. Menşur Tuğba Yalçin - Department of Mathematics, Faculty of Science and Arts, Kirikkale University, 71450 Yahsihan, Kirikkale, Turkey.


Abstract

The simulation function is defined by Khojasteh et al. [F. Khojasteh, S. Shukla, S. Radenović, 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. Karapınar, F. Khojasteh, A. F. Roldán-López-de-Hierro, Discrete Dyn. Nat. Soc., 2014 (2014), 10 pages], [M. Olgun, Ö. Biçer, 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.


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