Abstract
We study the stability problems of the following unified iterative scheme involving a
φ
-strongly pseudocontractive mapping (or
φ
-hemicontractive mapping)
T
x
n
+
1
=
f
(
T
,
v
n
,
x
n
)
=
α
n
x
n
+
β
n
Tv
n
+
γ
n
u
n
in arbitrary Banach spaces. We apply our results to obtain stability of an iterative scheme for a family of
k
-selfmappings.