Summary: We prove strong convergence theorems for the Ishikawa iteration scheme involving quasi-nonexpansive multi-valued maps. We also construct an iteration scheme which removes a restrictive condition in [Y.-S. Song
and H.-J. Wang
, Comput. Math. Appl. 55, No. 12, 2999–3002 (2008; Zbl 1142.47344
)]. Our results provide an affirmative answer to B. Panyanak
’s question [Comput. Math. Appl. 54, No. 6, 872–877 (2007; Zbl 1130.47050
)] in a more general setting.