Approximating fixed point results for pseudo-contractive map and some remarks on demi-contractive map in the Banach space

The purpose of our paper is to present a few convergence results for the Krasnoselskii–Mann iteration and also the modified Krasnoselskii–Mann iteration used for approximating the fixed point of k-strictly pseudo contractive map in the Banach space, which can be derived from the corresponding convergence theorems in the class of non-expansive maps. Also, using the enrichment techniques for contractive type 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 pseudo-contractive and demi-contractive maps are an unsaturated class of mappings in the Banach space. Illustrative examples and numerical calculations are given to support the obtained results, which are in fact the generalizations of approximations results in the Banach space from the Hilbert space.