Remarks on a recent paper titled: “On the split common fixed point problem for strict pseudocontractive and asymptotically nonexpansive mappings in Banach spaces”

Abstract 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 uniformly convex 2-uniformly smooth real Banach space with Opial property best smoothness constant κ satisfying condition $0<\kappa < \frac{1}{\sqrt{2}}$ 0 < κ 1 2 , as more general than Hilbert spaces. A well-known example of is $E=l_{p}$ E = l p $2\leq p<\infty $ ≤ ∞ . It shown in this paper that, if E satisfies \leq then necessarily $l_{2}$ space. Furthermore, some important remarks concerning proof are presented.