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Research Article | Open Access

Application of fixed point result to solve integral equation in the setting of graphical Branciari ℵ-metric spaces

Rajagopalan Ramaswamy1( ), Gunaseelan Mani2
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam Bin Abdulaziz University, Alkharj 11942, Saudi Arabia
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602 105, Tamil Nadu, India
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Abstract

In this present paper, we introduce graphical Branciari ℵ-metric space and prove the fixed point theorem for Ω- Q-contraction on complete graphical Branciari ℵ -metric spaces. Our result has been supplemented with suitable, non trivial examples. We have applied the derived fixed point result to solve non-linear Fredholm integral equations and fractional differential equation.

Keywords

Branciari ℵ-metric spacegraphical Branciari ℵ-metric spaceΩ-Q-contraction
CLC number: 47H10, 54H25

References

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AIMS Mathematics
Volume 9 Issue 11,
November 2024
Pages 32945-32961
DOI: 10.3934/math.20241576

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Ramaswamy R, Mani G. Application of fixed point result to solve integral equation in the setting of graphical Branciari ℵ-metric spaces. AIMS Mathematics, 2024, 9(11): 32945-32961. https://doi.org/10.3934/math.20241576

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Received: 12 September 2024
Revised: 04 November 2024
Accepted: 11 November 2024
Published: 21 November 2024
©2024 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)