Convergence of infinite family of multivalued quasi-nonexpansive mappings using multistep iterative processes (Q1724946)

Summary: We prove strong and weak convergence results using multistep iterative sequences for countable family of multivalued quasi-nonexpansive mappings by using some conditions in uniformly convex real Banach space. The results presented extended and improved the corresponding result of \textit{F. Zhang} et al. [J. Appl. Math. 2013, Article ID 649537, 7 p. (2013; Zbl 1266.47101)], \textit{A. Bunyawat} and \textit{S. Suantai} [Abstr. Appl. Anal. 2012, Article ID 435790, 6 p. (2012; Zbl 1237.47068)], and some others from finite family, one countable family, and two countable families to \(k\)-number of countable families of multivalued quasi-nonexpansive mappings. Also we use a numerical example in \texttt{C++} computational programs to prove that the iterative scheme we used has better rate of convergence than other existing iterative schemes.