TY - JOUR
T1 - Convergence of Ishikawa's iteration method for pseudocontractive mappings
AU - Zegeye, Habtu
AU - Shahzad, Naseer
AU - Alghamdi, Mohammad A.
PY - 2011/12/1
Y1 - 2011/12/1
N2 - Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→C,i=1,2,⋯,N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa's method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on T or on C. Moreover, computation of the closed convex set Cn for each n<1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings.
AB - Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→C,i=1,2,⋯,N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa's method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on T or on C. Moreover, computation of the closed convex set Cn for each n<1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings.
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U2 - 10.1016/j.na.2011.07.048
DO - 10.1016/j.na.2011.07.048
M3 - Article
AN - SCOPUS:80052814446
SN - 0362-546X
VL - 74
SP - 7304
EP - 7311
JO - Nonlinear Analysis, Theory, Methods and Applications
JF - Nonlinear Analysis, Theory, Methods and Applications
IS - 18
ER -