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 $E=l_{p}$ , $2\leq 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.

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最近一篇题为“关于Banach空间中严格的伪压缩和渐近非扩张映射的分裂公共不动点问题”的评论

在最近发表的关于严格伪收缩和渐近非扩张映射的分裂公共不动点问题的定理中，Tang等人。（J. Inequal。Appl。2015：305，2015）研究了具有Opial属性和满足条件$ 0 <\ kappa <\ frac {1} {\ sqrt {2}} $作为真正的Banach空间，比Hilbert空间更通用。带有Opial属性的均匀凸和2均匀平滑的实际Banach空间的一个著名示例是$ E = l_ {p} $，$ 2 \ leq p <\ infty $。本文表明，如果κ是E的最佳平滑度常数，并且满足条件$ 0 <\ kappa \ leq \ frac {1} {\ sqrt {2}} $，则E必然为$ l_ {2} $，一个真实的希尔伯特空间。此外，