A New Class of Asymmetric Quasi-Geraghty-Type Contraction Mappings with Applications to Non-Linear Differential Equations
A New Class of Asymmetric Quasi-Geraghty-Type Contraction Mappings with Applications tomNon-Linear...
DOI:
https://doi.org/10.63746/njtd.v23i2.4125Keywords:
Asymmetric contraction, Convergence, Differential and Integral equations, Fixed point, Geraghty-type mapping, StabilityAbstract
This paper introduces a new class of asymmetric quasi-Geraghty-type contraction mappings in the context of complete metric spaces. The study investigates the convergence, stability, and uniqueness of fixed points under the proposed mappings. We apply the new contraction principle to demonstrate the existence of solutions for several types of differential and integral equations, including Volterra integral equations, second-order boundary value problems, and nonlinear ordinary differential equations. Numerical illustrations validate the results and highlight the broader applicability of this approach compared to classical contraction mappings.
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