AbstractIn a recently published theorem on the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings, Tang et al. (J. Inequal. Appl. 2015:305, 2015) studied a uniformly convex and 2-uniformly smooth real Banach space with the Opial property and best smoothness constant κ satisfying the condition $0<\kappa < \frac{1}{\sqrt{2}}$
0
<
κ
<
1
2
, as a real Banach space more general than Hilbert spaces. A well-known example of a uniformly convex and 2-uniformly smooth real Banach space with the Opial property is $E=l_{p}$
E
=
l
p
, $2\leq p<\infty $
2
≤
p
<
∞
. It is shown in this paper that, if κ is the best smoothness constant of E and satisfies the condition $0<\kappa \leq \frac{1}{\sqrt{2}}$
0
<
κ
≤
1
2
, then E is necessarily $l_{2}$
l
2
, a real Hilbert space. Furthermore, some important remarks concerning the proof of this theorem are presented.