Let C be a nonempty closed convex subset of a real Hilbert space H and $$T: C\rightarrow CB(H)$$
T
:
C
→
C
B
(
H
)
be a multi-valued Lipschitz pseudocontractive nonself mapping. A Halpern–Ishikawa type iterative scheme is constructed and a strong convergence result of this scheme to a fixed point of T is proved under appropriate conditions. Moreover, an iterative method for approximating a fixed point of a k-strictly pseudocontractive mapping $$T: C\rightarrow Prox(H)$$
T
:
C
→
P
r
o
x
(
H
)
is constructed and a strong convergence of the method is obtained without end point condition. The results obtained in this paper improve and extend known results in the literature.
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