Fixed point theory in elliptic-valued metric spaces: applications to Fredholm integral equations and climate change analysis

Badriah Alamri; Badriah Alamri

doi:10.3934/math.2025641

AIMS Mathematics

2025, Volume 10, Issue 6: 14222-14247. doi: 10.3934/math.2025641

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Research article

Fixed point theory in elliptic-valued metric spaces: applications to Fredholm integral equations and climate change analysis

Badriah Alamri ^,

Department of Mathematics and Statistics, College of Science, University of Jeddah, Jeddah 23218, Saudi Arabia

Received: 25 February 2025 Revised: 29 April 2025 Accepted: 06 June 2025 Published: 23 June 2025
MSC : 46S40, 47H10, 54H25

The aim of this research article was to explore the framework of elliptic-valued metric spaces and establish novel common fixed point theorems for a wide range of generalized contraction mappings. Our findings provide a significant extension and unification of existing fixed point results, offering more refined mathematical tools for analyzing nonlinear problems in abstract spaces. To illustrate the effectiveness of our theorems, we present a concrete example that underscores the originality of our approach. Additionally, we highlight the practical significance of our main result by applying it to solve a nonlinear Fredholm integral equation of the second kind, which plays a crucial role in climate modeling. This equation is essential for understanding temperature distribution dynamics and feedback mechanisms within Earth's energy balance system. By bridging theoretical developments in metric space theory with real-world climate applications, this study contributes to both mathematical research and environmental science.
- fixed point,
- elliptic-valued metric space,
- self mappings,
- nonlinear Fredholm integral equations
Citation: Badriah Alamri. Fixed point theory in elliptic-valued metric spaces: applications to Fredholm integral equations and climate change analysis[J]. AIMS Mathematics, 2025, 10(6): 14222-14247. doi: 10.3934/math.2025641

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Abstract

The aim of this research article was to explore the framework of elliptic-valued metric spaces and establish novel common fixed point theorems for a wide range of generalized contraction mappings. Our findings provide a significant extension and unification of existing fixed point results, offering more refined mathematical tools for analyzing nonlinear problems in abstract spaces. To illustrate the effectiveness of our theorems, we present a concrete example that underscores the originality of our approach. Additionally, we highlight the practical significance of our main result by applying it to solve a nonlinear Fredholm integral equation of the second kind, which plays a crucial role in climate modeling. This equation is essential for understanding temperature distribution dynamics and feedback mechanisms within Earth's energy balance system. By bridging theoretical developments in metric space theory with real-world climate applications, this study contributes to both mathematical research and environmental science.

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