Generalized Rational Suzuki-Type Contractions in Double Controlled Metric Spaces with Applications
Abstract
In this paper, we introduce a new class of generalized rational Suzuki-type contractions in the setting of double controlled metric spaces. This framework extends controlled metric spaces by incorporating two independent control functions, thereby providing a more flexible structure for the analysis of nonlinear mappings. We establish an existence and uniqueness theorem for fixed points under this new contractive condition, which unifies and generalizes several known results in metric, $b$-metric, and controlled metric spaces. In addition, we investigate fundamental properties of the proposed framework, including a characterization via Picard iteration, Ulam--Hyers stability, convergence rate estimates, and data dependence of fixed points. As an application, we study the existence and uniqueness of solutions to a nonlinear Fredholm integral equation, showing that the proposed approach accommodates nonlinear kernels under weaker conditions than classical methods. The results contribute to the development of fixed point theory in generalized metric structures and provide a robust analytical tool for nonlinear problems arising in applied mathematics.
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