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

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