\(S-\gamma-\phi-\varphi\)-contractive type mappings in \(S\)-metric spaces

Volume 10, Issue 4, pp 1613--1639 http://dx.doi.org/10.22436/jnsa.010.04.27

Publication Date: April 20, 2017 Submission Date: October 26, 2016

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Authors

Mi Zhou - School of Science and Technology, Sanya College, 572022, Sanya, Hainan, China. Xiao-lan Liu - College of Science, Sichuan University of Science and Engineering, 643000, Zigong, Sichuan, China. - Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, Zigong, Sichuan 643000, China. Stojan Radenovic - Faculty of Mechanical Engineering, University of Belgrade, Kraljice Marije 16, 11120 Beograd, Serbia.

Abstract

In this paper, we introduce several types of \(S-\gamma-\phi-\varphi\)-contractive mappings which are generalizations of \(\alpha-\psi\) -contractive mappings [B. Samet, C. Vetro, P. Vetro, Nonlinear Anal., 75 (2012), 2154–2165] in the structure of S-metric spaces. Furthermore, we prove existence and uniqueness of fixed points and common fixed points of such contractive mappings. Our results generalize, extend and improve the existing results in the literature. We also state some illustrative examples to support our results.

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Keywords

• S-metric space
• \(S-\gamma-\phi-\varphi\)-contractive mappings
• fixed point.

MSC

•  47H10
•  54H25
•  54E50

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