Hai Yun ZHOU
In this paper, it is shown that there is a gap in the paper [Chidume, C. E., Shahzad, N.: Weak convergence theorems for a finite family of strict pseudo-contractions. Nonlinear Anal., 72, 1257-1265 (2010)], consequently, the main results of the paper do not hold in uniformly smooth Banach spaces. Meanwhile, it is also shown that the main results (Lemma 3.4, Theorems 3.5-3.6, 3.8-3.9) in the paper [Cholamjiak, P., Suantai, S.: Weak convergence theorems for a countable family of strict pseudo-contractions in Banach spaces. Fixed Point Theory Appl., 2010, Article ID 632137, 16 pages (2010)] do not hold in Lp for p > 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lp for p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above.
0 be a small function of f(z), and n ≥ 2 be a positive integer. If fn(z) and (fn(z))' share Q(z) CM, then f(z) = ce(1/n)z, where c is a nonzero constant. This result extends Lv's result from the case of polynomial to small entire function.
