In 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}}, 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}, 2leq p<infty . 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}}, then E is necessarily l_{2}, a real Hilbert space. Furthermore, some important remarks concerning the proof of this theorem are presented.