TY - JOUR
T1 - On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces
AU - Shahzad, Naseer
AU - Zegeye, Habtu
PY - 2009/8/1
Y1 - 2009/8/1
N2 - We prove strong convergence theorems for the Ishikawa iteration scheme involving quasi-nonexpansive multi-valued maps. We also construct an iteration scheme which removes a restrictive condition in Song and Wang results [Y. Song, H. Wang, Erratum to "Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces" [Comput. Math. Appl. 54 (2007) 872-877], Comput. Math. Appl. 55 (2008) 2999-3002]. Our results provide an affirmative answer to Panyanak's question [Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comput. Math. Appl., 54 (2007), 872-877], in a more general setting.
AB - We prove strong convergence theorems for the Ishikawa iteration scheme involving quasi-nonexpansive multi-valued maps. We also construct an iteration scheme which removes a restrictive condition in Song and Wang results [Y. Song, H. Wang, Erratum to "Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces" [Comput. Math. Appl. 54 (2007) 872-877], Comput. Math. Appl. 55 (2008) 2999-3002]. Our results provide an affirmative answer to Panyanak's question [Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comput. Math. Appl., 54 (2007), 872-877], in a more general setting.
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U2 - 10.1016/j.na.2008.10.112
DO - 10.1016/j.na.2008.10.112
M3 - Article
AN - SCOPUS:67349177159
SN - 0362-546X
VL - 71
SP - 838
EP - 844
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 3-4
ER -