Convergence of Graph-Based Fixed Point Results with Application to Fredholm Integral Equation

Haroon Ahmad, Aqsa Riaz, Mahpeyker Öztürk (), Fahim Ud Din, Mehmet Emir Köksal and Ekber Girgin
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Haroon Ahmad: Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
Aqsa Riaz: Department of Mathematics and Statistics, Faculty of Science, University of Lahore, Lahore 54590, Pakistan
Mahpeyker Öztürk: Department of Mathematics, Sakarya University, 54050 Sakarya, Turkey
Fahim Ud Din: Abdus Salam School of Mathematical Sciences, Government College University, Lahore 54600, Pakistan
Mehmet Emir Köksal: Department of Mathematics, Ondokuz Mayis University, 55139 Atakum, Turkey
Ekber Girgin: Department of Engineering Fundamental Sciences, Sakarya University of Applied Sciences, 54187 Sakarya, Turkey

Mathematics, 2024, vol. 12, issue 20, 1-14

Abstract: In this manuscript, we present a novel concept termed graphical Θ c -Kannan contraction within the context of graphically controlled metric-type spaces. Unlike traditional Kannan contraction, this novel concept presents a modified method of contraction mapping. We discuss the significance and the existence of fixed point results within the framework of this novel contraction. To strengthen the credibility of our theoretical remarks, we provide a comparison example demonstrating the efficiency of our suggested framework. Our study not only broadens the theoretical foundations inside graphically controlled metric-type spaces by introducing and examining visual Θ c -Kannan contraction, but it also demonstrates the practical significance of our innovations through significant examples. Furthermore, applying our findings to second-order differential equations by constructing integral equations into the domain of Fredholm sheds light on the broader implications of our research in the field of mathematical analysis and contributes to the advancement of this field.

Keywords: directed graph; fixed point; graphic contraction; graphically controlled metric-type space; Fredholm integral equation (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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