EXISTENCE AND ESTIMATION OF THE FIXED POINTS OF ENRICHED BERINDE NONEXPANSIVE MAPPINGS

In this article, inspired by Berinde (Approximating fixed points of enriched nonexpansive mappings by Krasnoselskii iteration in Hilbert spaces, Carpathian J. Math. 35(3), 2019, 293-304), we define and study a new enriched class of mappings which includes many other contractive type mappings. We prove an existence result for the fixed point of newly introduced mapping. We also estimate fixed points of the proposed mapping via newly modified Mann iteration. In the process, some convergence results are also obtained for the proposed class of mappings in Uniformly convex Banach space.