Coupled fixed points of generalized rational type Z-contraction maps in b-metric spaces

Document Type : Research Paper

Authors

1 Department of Mathematics, Acharya Nagarjuna University, Guntur - 522 510, India

2 Department of Mathematics, PSCMRCET, Vijayawada - 520 001, India

3 Department of Mathematics, Rayalaseema University, Kurnool - 518 007, India

4 Department of Mathematics, PBR VITS, Kavali- 524 201, India

Abstract

In this paper, we introduce generalized rational type $\mathcal{Z}$-contraction maps for a single map $f:X\times X\to X$ where $X$ is a $b$-metric space and prove the existence and uniqueness of coupled fixed points. We extend it to a pair of maps by defining generalized rational type $\mathcal{Z}$-contraction pair of maps and prove the existence of common coupled fixed points in complete $b$-metric spaces. We provide examples in support of our results.

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