Convergence of SP-iteration for generalized nonexpansive mapping in Banach spaces
Javid Ali, Izhar Uddin · Ukrains’kyi Matematychnyi Zhurnal · 2021
UDC 517.9 Phuengrattana and Suantai [J. Comput. and Appl. Math., 235, 3006 – 3014 (2011)] introduced an iteration scheme and they named this iteration as SP-iteration. In this paper, we study the convergence behaviour of SP-iteration scheme for the class of generalized nonexpansive mappings. One weak convergence theorem and two strong convergence theorems in uniformly convex Banach spaces are obtained. We also furnish a numerical example in support of our main result. In process, our results generalize and improve many existing results in the literature.