A fixed point approach to predator-prey dynamics via nonlinear mixed Volterra–Fredholm integral equations in complex-valued suprametric spaces

Afrah Ahmad Noman Abdou; Afrah Ahmad Noman Abdou

doi:10.3934/math.2025274

AIMS Mathematics

2025, Volume 10, Issue 3: 6002-6024. doi: 10.3934/math.2025274

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Research article

A fixed point approach to predator-prey dynamics via nonlinear mixed Volterra–Fredholm integral equations in complex-valued suprametric spaces

Afrah Ahmad Noman Abdou ^,

Department of Mathematics and Statistics, Faculty of Science, University of Jeddah, P. O. Box 80327, Jeddah 21589, Saudi Arabia

Received: 23 December 2024 Revised: 03 February 2025 Accepted: 14 February 2025 Published: 18 March 2025
MSC : 46S40, 47H10, 54H25

This study explores the concept of complex-valued suprametric spaces, a recent and generalized framework in fixed point theory. This concept extends both complex-valued spaces and classical metric spaces. The article aims to establish common fixed point results for rational contractions governed by control functions dependent on two variables within the setting of complex-valued suprametric spaces. These findings generalize several well-known results in the field. An illustrative example is provided to validate the novelty of the key result. Furthermore, the study derives common fixed point theorems for rational contractions with control functions of a single variable under the same framework. As a practical application, the findings are applied to study the solution of a nonlinear mixed Volterra–Fredholm integral equation within the context of predator-prey dynamics.
- complex-valued suprametric spaces,
- common fixed point,
- control functions,
- Volterra–Fredholm integral equation,
- rational expressions,
- predator-prey dynamics
Citation: Afrah Ahmad Noman Abdou. A fixed point approach to predator-prey dynamics via nonlinear mixed Volterra–Fredholm integral equations in complex-valued suprametric spaces[J]. AIMS Mathematics, 2025, 10(3): 6002-6024. doi: 10.3934/math.2025274

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Abstract

This study explores the concept of complex-valued suprametric spaces, a recent and generalized framework in fixed point theory. This concept extends both complex-valued spaces and classical metric spaces. The article aims to establish common fixed point results for rational contractions governed by control functions dependent on two variables within the setting of complex-valued suprametric spaces. These findings generalize several well-known results in the field. An illustrative example is provided to validate the novelty of the key result. Furthermore, the study derives common fixed point theorems for rational contractions with control functions of a single variable under the same framework. As a practical application, the findings are applied to study the solution of a nonlinear mixed Volterra–Fredholm integral equation within the context of predator-prey dynamics.

References

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