Existence of fixed points for \(\gamma\)-\(FG\)-contractive condition via cyclic \((\alpha,\beta)\)-admissible mappings in \(b\)-metric spaces

Volume 10, Issue 10, pp 5495--5508 http://dx.doi.org/10.22436/jnsa.010.10.31

Publication Date: October 31, 2017 Submission Date: March 21, 2017

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Authors

Saroj Kumar Padhan - Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Sambalpur, Odisha-768018, INDIA. G V V Jagannadha Rao - Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Sambalpur, Odisha-768018, INDIA. Ahmed Al-Rawashdeh - Department of Mathematical sciences, UAE University, 1555, Al Ain, U.A.E. Hemant Kumar Nashine - Department of Mathematics, Texas A \(\&\) M University, Kingsville-78363-8202, Texas, U.S.A. Ravi P. Agarwal - Department of Mathematics, Texas A \(\&\) M University, Kingsville-78363-8202, Texas, U.S.A.

Abstract

In this paper, we introduce a new concept of cyclic \((\alpha,\beta)\)-type \(\gamma\)-\(FG\)-contractive mapping and we prove some fixed point theorems for such mappings in complete \(b\)-metric spaces. Suitable examples are introduced to verify the main results. As an application, we obtain sufficient conditions for the existence of solutions for nonlinear integral equation which are illustrated by an example.

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Keywords

• \(b\)-metric space
• cyclic \((\alpha
• \beta)\)-admissible
• \(\gamma\)-\(FG\)-contractive

MSC

•  47H09
•  54H25
•  47H10

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