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Weak convergence theorems for strict pseudo-contractions in Banach spaces.
- Source :
-
Acta Mathematica Sinica . May2014, Vol. 30 Issue 5, p755-766. 12p. - Publication Year :
- 2014
-
Abstract
- 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 L for p > 3. Finally, some modified results are presented in the setting of uniformly smooth and uniformly convex Banach spaces which include L for p ≥ 2 as special cases. Furthermore, our arguments are also different from the ones given by the authors above. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14398516
- Volume :
- 30
- Issue :
- 5
- Database :
- Academic Search Index
- Journal :
- Acta Mathematica Sinica
- Publication Type :
- Academic Journal
- Accession number :
- 95593458
- Full Text :
- https://doi.org/10.1007/s10114-014-3096-5