On a first investigation of Hausdorff interpolative metric spaces with applications to fractal geometry and market equilibrium

In this paper, we aim to establish several properties and notions for interpolative metric spaces and to introduce the idea of a Hausdorff interpolative metric space. Through the formulation of the key principles of Hausdorff interpolative metric spaces, we present the notion of Hutchinson-type operators and ws-Hutchinson operators. We then establish fixed point results and discuss their applications in fractal geometry, particularly focusing on various forms of the Sierpiński triangles and regular pentagon. Several examples are provided to illustrate the applicability of our findings. We also discuss the existence and provide conditions ensuring the uniqueness of solutions for market equilibrium models formulated as fractional differential equations. This approach not only supports the stability of these models but also reinforces the foundation for steady and sustainable economic development. Our results serve as proper generalizations of various contractions in the context of interpolative metric spaces.