LET E be a real Banach space with norm ||·||,E~* a uniformly convex dual space.Let K bea nonempty closed convex and bounded subset of E,T:K→K a continuous strongly pseudo-contractive mapping.Recently,Chidume pro...LET E be a real Banach space with norm ||·||,E~* a uniformly convex dual space.Let K bea nonempty closed convex and bounded subset of E,T:K→K a continuous strongly pseudo-contractive mapping.Recently,Chidume proved that the Mann iterative sequence of contin-展开更多
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）], consequ...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 Lpfor p 〉 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lpfor p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above.展开更多
In this paper, by using new analysis techniques, we have studied iterative construc- tion problem for finding zeros of accretive mappings in uniformly smooth Banach spaces, and improved a theorem due to Reich. As its ...In this paper, by using new analysis techniques, we have studied iterative construc- tion problem for finding zeros of accretive mappings in uniformly smooth Banach spaces, and improved a theorem due to Reich. As its application, we have deduced a strong convergence theorem of fixed points for continuous pseudo-contractions.展开更多
文摘LET E be a real Banach space with norm ||·||,E~* a uniformly convex dual space.Let K bea nonempty closed convex and bounded subset of E,T:K→K a continuous strongly pseudo-contractive mapping.Recently,Chidume proved that the Mann iterative sequence of contin-
基金Supported by National Natural Science Foundation of China(Grant Nos.10771050,11071053)
文摘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 Lpfor p 〉 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include Lpfor p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above.
基金the National Natural Science Foundation of China (No.10471033)
文摘In this paper, by using new analysis techniques, we have studied iterative construc- tion problem for finding zeros of accretive mappings in uniformly smooth Banach spaces, and improved a theorem due to Reich. As its application, we have deduced a strong convergence theorem of fixed points for continuous pseudo-contractions.
