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

Abhishikta Das, Hemanta Kalita, Mohammad Sajid, T. Bag

Published 2025-04-22, updated 2025-05-05Version 2

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.