Coupled Fixed Points for Hardy-Rogers Type of Maps and Their Applications in the Investigations of Market Equilibrium in Duopoly Markets for Non-Differentiable, Nonlinear Response Functions

TL;DR

This paper extends Hardy-Rogers maps to coupled fixed points and applies the results to analyze market equilibrium in duopoly markets with non-differentiable, nonlinear response functions, providing new theoretical insights.

Contribution

It generalizes Hardy-Rogers maps for coupled fixed points and applies these to establish existence and uniqueness of market equilibrium in complex duopoly models.

Findings

Established conditions for market equilibrium existence and uniqueness.

Extended Hardy-Rogers maps to non-differentiable, nonlinear response functions.

Provided a framework for analyzing duopoly markets with generalized response functions.

Abstract

In this paper we generalize Hardy-Rogers maps in the context of coupled fixed points. We generalizes with the help of the obtained main theorem some known results about existence and uniqueness of market equilibrium in duopoly markets. We investigate some recent results about market equilibrium in duopoly markets with the help of the main theorem and we enrich them. We define a generalized response function including production and surpluses. Finally we illustrate a possible application of the main result in the investigation of market equilibrium, when the pay off functions are non differentiable.