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Research Article | Open Access

Solving a nonlinear integral equation via orthogonal metric space

Arul Joseph Gnanaprakasam1, Gunaseelan Mani2, Jung Rye Lee3( ), Choonkil Park4( )
Department of Mathematics, College of Engineering and Technology, SRM Institute of Science and Technology, SRM Nagar, Kattankulathur, Kanchipuram, Chennai, Tamil Nadu 603 203, India
Department of Mathematics, Sri Sankara Arts and Science College (Autonomous), Affiliated to Madras University, Enathur, Kanchipuram, Tamil Nadu 631 561, India
Department of Data Science, Daejin University, Kyunngi 11159, Korea
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
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Abstract

We propose the concept of orthogonally triangular α-admissible mapping and demonstrate some fixed point theorems for self-mappings in orthogonal complete metric spaces. Some of the well-known outcomes in the literature are generalized and expanded by our results. An instance to help our outcome is presented. We also explore applications of our key results.

Keywords

orthogonal setorthogonal complete metric spaceorthogonal continuousorthogonal preservingorthogonally triangular α-admissiblefixed point
CLC number: 47H10, 54H25

References

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AIMS Mathematics
Volume 7 Issue 1,
January 2022
Pages 1198-1210
DOI: 10.3934/math.2022070

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Cite this article:
Gnanaprakasam AJ, Mani G, Lee JR, et al. Solving a nonlinear integral equation via orthogonal metric space. AIMS Mathematics, 2022, 7(1): 1198-1210. https://doi.org/10.3934/math.2022070

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Received: 07 July 2021
Accepted: 11 October 2021
Published: 15 January 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)