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2012 Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators
C. E. Chidume, N. Djitté
Abstr. Appl. Anal. 2012(SI12): 1-19 (2012). DOI: 10.1155/2012/681348


An iteration process studied by Chidume and Zegeye 2002 is proved to converge strongly to a solution of the equation A u = 0 where A is a bounded m-accretive operator on certain real Banach spaces E that include L p spaces 2 p < ∞. The iteration process does not involve the computation of the resolvent at any step of the process and does not involve the projection of an initial vector onto the intersection of two convex subsets of E, setbacks associated with the classical proximal point algorithm of Martinet 1970, Rockafellar 1976 and its modifications by various authors for approximating of a solution of this equation. The ideas of the iteration process are applied to approximate fixed points of uniformly continuous pseudocontractive maps.


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C. E. Chidume. N. Djitté. "Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators." Abstr. Appl. Anal. 2012 (SI12) 1 - 19, 2012.


Published: 2012
First available in Project Euclid: 1 April 2013

zbMATH: 1254.47035
MathSciNet: MR2903815
Digital Object Identifier: 10.1155/2012/681348

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI12 • 2012
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