Fixed point theorems for generalized \(\alpha\)-\(\psi\) type contractive mappings in b-metric spaces and applications

Volume 18, Issue 1, pp 49--62 http://dx.doi.org/10.22436/jmcs.018.01.06

Publication Date: December 31, 2017 Submission Date: November 01, 2016

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Authors

Xianbing Wu - Department of Mathematics, Yangtze Normal University, Fuling, Chongqing 408100, P. R. China Leina Zhao - College of Mathematics and Statistics, Chongqing Jiaotong University, Chongqing, 400074, P. R. China

Abstract

In this paper, we establish fixed point theorems for a new generalized \(\alpha\)-\(\psi\) type contractive mapping in complete b-metric spaces. As applications of our results, we obtain fixed point theorems on metric space endowed with a partial order or a graph. We also obtain fixed point theorems for cyclic contractive mappings. Moreover, an application to integral equation is given here to illustrate the usability of the obtained results.

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Keywords

• \(\alpha\)-\(\psi\) contractive mapping
• b-metric space
• fixed point theorem

MSC

•  47H10
•  47H09
•  49J40

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