A methodology of hybrid fixed point theorems for solving Fredholm-Volterra integral equations

Volume 41, Issue 3, pp 334--346 https://dx.doi.org/10.22436/jmcs.041.03.04

Publication Date: November 12, 2025 Submission Date: April 02, 2025 Revision Date: August 17, 2025 Accteptance Date: September 05, 2025

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Authors

M. S. Shagari - Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria. P. Oloche - Department of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria. M. Noorwali - Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia. I. Ayoob - Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia. N. Mlaiki - Department of Mathematics and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia.

Abstract

This paper studies a new notion of Jaggi-type hybrid (\(\theta\)-\(\phi\))-contraction and demonstrates its roles in proving fixed point theorems within the context of a generalized metric space. We prove, using comparative examples that under special instances, the ideas presented herein can be reduced to some known results in the existing literature. To show a possible application of our main contractive inequality, iterative methods are developed for addressing the existence of solutions to a class of mixed nonlinear fixed point problems involving Volterra-Fredholm integral equation.

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Keywords

• Fixed point
• metric space
• \(\theta\)-contraction
• nonlinear integral equation
• Volterra-Fredholm integral

MSC

•  47H10
•  47H25
•  54H25

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