Fixed point theorems for enriched C´iric´ quasi contraction map in Banach and convex metric spaces

Abstract

The purpose of our paper is to present some fixed point results for enriched C´iric´ quasi-contraction map in the Banach space and convex metric space. Using enrichment techniques for contractive types map T, i.e., the averaged operator Tλ(u)=(1-λ)u+λTu, where λ∈(0,1], we identified that C´iric´ quasi-contraction is an unsaturated class of mappings in the Banach space. Furthermore, we present here enriched cyclic C´iric´ quasi-contraction results in the Banach space so that fractal theory can be generated. © The Indian National Science Academy 2024.