Fixed Points on Covariant and Contravariant Maps with an Application

Abstract

Fixed-point results on covariant maps and contravariant maps in a (Formula presented.) -algebra-valued bipolar metric space are proved. Our results generalize and extend some recently obtained results in the existing literature. Our theoretical results in this paper are supported with suitable examples. We have also provided an application to find an analytical solution to the integral equation and the electrical circuit differential equation.