Fixed points for $G$-cyclic $(\phi -\psi)$-Kannan and $G$-cyclic $(\phi -\psi)$-Chatterjea contractions in $G$-metric spaces

Abstract

Definitions of what are called $G$-cyclic $\left( \phi -\psi \right)$-Kannan contraction and $G$-cyclic $\left( \phi -\psi\right)$-Chatterjea contraction are introduced in this paper. We use these new concepts to establish new fixed point results in the context of complete generalized metric spaces. These results are new generalizations and extensions of the Kannan and Chatterjea fixed point theorems and are generalized versions of some fixed point results proved in the literature. The analysis and theory are illustrated by some examples.