On a New Stochastic Space with Applications to Nonlinear Economic Models

Abstract

This article will utilize a weighted regular matrix composed of Fibonacci numbers and variable exponent sequence spaces to create a novel stochastic space with certain geometric and topological properties. This area demonstrates the new form of the Kannan contraction operator with a fixed point. In mathematical economics, we represent economic entities, processes, and phenomena by mathematically structured functional equations, either as summable equations or integral equations. We investigate a category of Volterra-type non-linear dynamical systems, similar to an economic model. We employ our acquired results to formulate new solvability criteria for a unique solution of these non-linear discrete economic dynamical systems. Ultimately, we illustrate our findings with specific instances and applications related to the presence of solutions in non-linear dynamical systems of Volterra-type.