Let E be a uniformly convex Banach space with a uniformly G

ateaux differentiable norm, C a nonempty closed convex subset of E, and T : C

K(E) a multivalued nonself-mapping such that

is nonexpansive, where

(x) = {

Tx : llx -

ll = d(x, Tx)g. For f : C

C a contraction and t

(0; 1), let

be a fixed point of a contraction

: C

K(E), defined by

:=

, x

C. It is proved that if C is a nonexpansive retract of E and {

} is bounded, then the strong

exists and belongs to the fixed point set of T. Moreover, we study the strong convergence of {

} with the weak inwardness condition on T in a reflexive Banach space with a uniformly G

teaux differentiable norm. Our results provide a partial answer to Jung's question.