Abstract
Let
C
be a nonempty, closed and convex subset of a real Hilbert space
H
. Let
T
i
:
C
→
H
,
i
=
1
,
2
,
…
,
N
, be a finite family of generalized asymptotically nonexpansive mappings. It is our purpose, in this paper to prove strong convergence of Mann’s type method to a common fixed point of
{
T
i
:
i
=
1
,
2
,
…
,
N
}
provided that the interior of common fixed points is nonempty. No compactness assumption is imposed either on
T
or on
C
. As a consequence, it is proved that Mann’s method converges for a fixed point of nonexpansive mapping provided that interior of
F
(
T
)
≠
0̸
. The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings.