Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an Application

Abstract

This study aims to provide some new classes of (α,β,F*)-weak Geraghty contraction and (α,β,F**)-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we find that the mappings satisfying the definition of such contractions have a unique fixed point if the underlying space is complete. In addition, we provide an application showing the uniqueness of the solution of the two-point boundary value problem.

Keywords

• fixed point
• <i>F</i>-contraction
• <i>α</i>-admissible mapping
• (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-weak Geraghty contractions