Let E be a closed, bounded, convex subset of a Banach space
X
,
f
:
E
→
E
X,f:E \to E
. Consider the iteration scheme defined by
x
¯
0
=
x
0
∈
E
,
x
¯
n
+
1
=
f
(
x
n
)
,
x
n
=
Σ
k
=
0
n
a
n
k
x
¯
k
,
n
≥
1
{\bar x_0} = {x_0} \in E,{\bar x_{n + 1}} = f({x_n}),{x_n} = \Sigma _{k = 0}^n{a_{nk}}{\bar x_k},\;n \geq 1
, where A is a regular weighted mean matrix. For particular spaces X and functions f we show that this iterative scheme converges to a fixed point of f.