Common Fixed Point Theorems For F-Contractions In $G$-Metric Spaces Using Compatible Mappings

Abstract

Using a mapping $F:\mathbb{R_{+}}\rightarrow \mathbb{R}$, Wardowski [1] introduce a new type of contraction called $F$-contraction and prove a new fixed point theorem concerning $F$-contraction. In the present article, we prove some fixed point theorems with helping compatible maps for type $1$ and type $2$ $F$-contraction in complete $G$-metric spaces.