Solving Integral Equation and Homotopy Result via Fixed Point Method

Abstract

The aim of the present research article is to investigate the existence and uniqueness of a solution to the integral equation and homotopy result. To achieve our objective, we introduce the notion of (α,η,ψ)-contraction in the framework of F-bipolar metric space and prove some fixed point results for covariant and contravariant mappings. Some coupled fixed point results in F-bipolar metric space are derived as outcomes of our principal theorems. A non-trivial example is also provided to validate the authenticity of the established results.

Keywords

• fixed point
• generalized contractions
• <i>?</i>-bipolar metric space
• integral equation
• homotopy