be a nonempty compact convex subset of a uniformly convex Banach space and let
be a multivalued nonexpansive mapping. We prove that the sequences of Mann and Ishikawa iterates converge to a fixed point of
. This generalizes former results proved by K. P. R. Sastry
and G. V. R. Babu
[Czech. Math. J. 55, No. 4, 817–826 (2005; Zbl 1081.47069
)]. We also introduce both of the iterative processes in a new sense, and prove a convergence theorem of Mann iterates for a mapping defined on a noncompact domain.