Convergence of Ishikawa’s iteration method for pseudocontractive mappings |
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Authors: | Habtu Zegeye Naseer Shahzad Mohammad A. Alghamdi |
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Affiliation: | aDepartment of Mathematics, University of Botswana, Pvt. Bag 00704 Gaborone, Botswana;bDepartment of Mathematics, King Abdul Aziz University, P.O.B. 80203, Jeddah 21589, Saudi Arabia |
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Abstract: | 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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Keywords: | MSC: 47H05 47H09 47H10 47J05 47J25 |
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