Some common fixed point theorems in bipolar metric spaces and applications

Joginder Paul; Mohammad Sajid; Naveen Chandra; Umesh Chandra Gairola; Joginder Paul; Mohammad Sajid; Naveen Chandra; Umesh Chandra Gairola

doi:10.3934/math.2023969

AIMS Mathematics

2023, Volume 8, Issue 8: 19004-19017. doi: 10.3934/math.2023969

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Research article

Some common fixed point theorems in bipolar metric spaces and applications

1.
Department of Mathematics, H. N. B. Garhwal University, B. G. R. Campus, Pauri-246001, Uttarakhand, India
2.
Department of Mechanical Engineering, College of Engineering, Qassim University, Buraydah-51452, Saudi Arabia

Received: 24 March 2023 Revised: 18 May 2023 Accepted: 28 May 2023 Published: 06 June 2023
MSC : 47H10, 54H25

In this article, we prove some common fixed point theorems for generalized rational type contractions in bipolar metric spaces. These theorems also generalize and extend several interesting results of metric fixed point theory to the bipolar metric context. In addition, we provide some examples to illustrate our theorems, and applications are obtained in areas of homotopy theory and integral equations by using iterative methods for mathematical operators on a bipolar metric space.
- common fixed point,
- rational type contraction,
- bipolar metric spaces,
- iterative methods,
- mathematical operators
Citation: Joginder Paul, Mohammad Sajid, Naveen Chandra, Umesh Chandra Gairola. Some common fixed point theorems in bipolar metric spaces and applications[J]. AIMS Mathematics, 2023, 8(8): 19004-19017. doi: 10.3934/math.2023969

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Abstract

In this article, we prove some common fixed point theorems for generalized rational type contractions in bipolar metric spaces. These theorems also generalize and extend several interesting results of metric fixed point theory to the bipolar metric context. In addition, we provide some examples to illustrate our theorems, and applications are obtained in areas of homotopy theory and integral equations by using iterative methods for mathematical operators on a bipolar metric space.

References

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