New Geraghty type contractions on metric-like spaces

Volume 10, Issue 2, pp 780--788 http://dx.doi.org/10.22436/jnsa.010.02.38

Publication Date: February 20, 2017 Submission Date: November 26, 2016

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Authors

Hassen Aydi - Department of Mathematics, College of Education of Jubail, University of Dammam, P. O. 12020, Industrial Jubail 31961, Saudi Arabia. - Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan. Abdelbasset Felhi - Department of Mathematics and Statistics, College of Sciences, King Faisal University, Hafouf, Saudi Arabia. Hojjat Afshari - Faculty of Basic Science, University of Bonab, Bonab, Iran.

Abstract

Very recently, Fulga and Proca [A. Fulga, A. M. Proca, Abstr. Appl. Anal., (In press)] considered new Geraghty type contraction mappings and established a fixed point theorem for such mappings in complete metric spaces. In this paper, we prove the analogous result in the class of metric-like spaces which generalizes the main result of Karapinar et al. [E. Karapınar, H. H. Alsulami, M. Noorwali, Fixed Point Theory Appl., 2015 (2015), 22 pages]. We give some examples illustrating the presented result where [E. Karapınar, H. H. Alsulami, M. Noorwali, Fixed Point Theory Appl., 2015 (2015), 22 pages] is not applicable. An application is also provided.

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Keywords

• Fixed point
• Geraghty type contraction
• metric-like space.

MSC

•  47H10
•  54H25

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