Fixed point theorems for enriched \(\acute{C}\)iri\(\acute{c}\) quasi contraction map in Banach and convex metric spaces

The purpose of our paper is to present some fixed point results for enriched \(\acute{C}\) $\acute{C}$ iri \(\acute{c}\) $\acute{c}$ quasi-contraction map in the Banach space and convex metric space. Using enrichment techniques for contractive types map T, i.e., the averaged operator \(T_{\lambda }(u)=(1-\lambda )u+\lambda Tu\) $T_{\lambda }(u)=(1-\lambda )u+\lambda Tu$ , where \(\lambda \in (0,1]\) $\lambda \in (0,1]$ , we identified that \(\acute{C}\) $\acute{C}$ iri \(\acute{c}\) $\acute{c}$ quasi-contraction is an unsaturated class of mappings in the Banach space. Furthermore, we present here enriched cyclic \(\acute{C}\) $\acute{C}$ iri \(\acute{c}\) $\acute{c}$ quasi-contraction results in the Banach space so that fractal theory can be generated.