Generalized \(\mathit{Z}\)-contraction on quasi metric spaces and a fixed point result
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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.
Share and Cite
ISRP Style
Hakan Şimşek, Menşur Tuğba Yalçin, Generalized \(\mathit{Z}\)-contraction on quasi metric spaces and a fixed point result, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 7, 3397--3403
AMA Style
Şimşek Hakan, Yalçin Menşur Tuğba, Generalized \(\mathit{Z}\)-contraction on quasi metric spaces and a fixed point result. J. Nonlinear Sci. Appl. (2017); 10(7):3397--3403
Chicago/Turabian Style
Şimşek, Hakan, Yalçin, Menşur Tuğba. "Generalized \(\mathit{Z}\)-contraction on quasi metric spaces and a fixed point result." Journal of Nonlinear Sciences and Applications, 10, no. 7 (2017): 3397--3403
Keywords
- Quasi metric space
- left K-Cauchy sequence
- simulation functions
- fixed point.
MSC
References
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