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

TL;DR

This paper introduces generalized $ heta$-parametric metric spaces, extending fixed point theory and applying it to fractional economic models, with new theorems, properties, and practical economic applications.

Contribution

It develops a new class of metric spaces, establishes fixed point theorems within this framework, and demonstrates their application to fractional differential equations in economics.

Findings

Established fundamental properties of generalized $ heta$-metric spaces

Formulated Suzuki-type fixed point theorem in this context

Applied the theory to analyze economic growth 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.