Generalized $\theta$-Parametric Metric Spaces: Fixed Point Theorems and Applications to Fractional Economic Models

Abstract

The objective of this manuscript is to introduce and develop the concept of a generalized $\theta$-parametric metric space-a novel extension that enriches the modern metric fixed point theory. We study of its fundamental properties, including convergence and Cauchy sequences that establishes a solid theoretical foundation. A significant highlight of our work is the formulation of Suzuki-type fixed point theorem within this framework which extends classical results in a meaningful way. To demonstrate the depth and applicability of our findings, we construct non-trivial examples that illustrate the behavior of key concepts. Moreover, as a practical application, we apply our main theorem to analyze an economic growth model, demonstrating its utility in solving fractional differential equations that arise in dynamic economic systems.

arXiv comment23 pages

References in corpus (1)

• Vietoris-Rips Persistent Homology, Injective Metric Spaces, and The Filling Radius