Iterative algorithms for a finite family of multivalued quasi-nonexpansive mappings (Q2260477)

Summary: Let \(K\) be a nonempty closed and convex subset of a uniformly convex real Banach space \(E\) and let \(T_1, \dots, T_m : K \to 2^K\) be \(m\) multivalued quasi-nonexpansive mappings. A new iterative algorithm is constructed and the corresponding sequence \(\{x_n\}\) is proved to be an approximating fixed point sequence of each \(T_i\); that is, \(\lim d(x_n;Tx_n)=0\). Then, convergence theorems are proved under appropriate additional conditions. Our results extend and improve some important recent results (e.g., [\textit{M. Abbas} et al., Appl. Math. Lett. 24, No. 2, 97--102 (2011; Zbl 1223.47068)]).