Asymptotic stability of equilibria for difference equations via fixed points of enriched Prešić operators

Abstract

We introduced a new general class of Prešić-type operators, by enriching the known class of Prešić contractions. We established conditions under which enriched Prešić operators possess a unique fixed point, proving the convergence of two different iterative methods to the fixed point. We also gave a data dependence result that was finally applied in proving the global asymptotic stability of the equilibrium of a certain k-th order difference equation.

Keywords

• enriched prešić operator
• fixed point
• global asymptotic stability
• difference equation
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