Fixed point theorems for generalized contractions in $ \mathfrak{F} $-bipolar metric spaces with applications

Abstract

The major objectives of this research article are to introduce the notion of ($ \alpha, \psi $)-contraction in the context of $ \mathfrak{F} $-bipolar metric space and establish fixed point theorems. In this way, coupled fixed point results are obtained by applying the leading theorems. Some non-trivial examples are also furnished to show the validity of established results. As applications of the main result, we investigate the solution of an integral equation and a homotopy problem.

Keywords

• fixed point
• ($ \alpha
• \psi $)-contractions
• $ \mathfrak{f} $-bipolar metric space
• integral equation
• homotopy