Some Results for Ćirić–Prešić Type Contractions in <i>F</i>-Metric Spaces

Abstract

In this study, first, we introduce Ćirić–Prešić type contraction in F-metric spaces and prove a fixed point theorem for self mappings. We apply the fixed point results for a second-order differential equation. Therefore, we define Prešić type almost contraction and F-contraction, and we prove some fixed point theorems. In the last section, we prove the best proximity point theorems for Ćirić–Prešić type proximal contraction in F-metric spaces. Our results generalize the existing results in the literature.

Keywords

• almost contraction
• best proximity
• fixed point
• <i>F</i>-metric
• <i>F</i>-contraction