Application of Hybrid Fixed Point Theorems for (α,β)-admissible Mappings in Nonlinear Integral Equations of Controlled Metric Spaces
DOI:
https://doi.org/10.64137/3108-2637/IJMAR-V2I3P102Keywords:
Constraction, Nonlinear, Controlled Metric Space, (α,β)-Admissible Mapping, Hybrid Contraction, Fixed Point Theorem, Volterra-Fredholm Integral Equation, Existence and UniquenessAbstract
This paper introduces novel hybrid fixed point theorems for (α,β)-admissible mappings within the framework of controlled metric spaces. We establish the existence and uniqueness of fixed points for a special class of hybrid contractions that combine Ćirić-Reich-Rus type contractions with Suzuki-type conditions under weakened contraction hypotheses. The controlled metric space setting, being a significant abstraction of classical metric spaces, allows for more flexible distance measurements through control functions. Our main results extend many existing fixed point theorems in the literature and provide less restrictive sufficient conditions for the existence of fixed points. Furthermore, we demonstrate the applicability of our theoretical findings by establishing the existence and uniqueness of solutions to a special class of nonlinear Volterra-Fredholm integral equations arising in population dynamics and mathematical biology. Illustrative examples with numerical computations validate our theoretical results and demonstrate their practical utility.
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