Strong Convergence Theorems for Zeros of Bounded Maximal Monotone Nonlinear Operators. (27th March 2012)

• Record Type: Journal Article
• Authors: Chidume, C. E.; Djitté, N.
• Other Names: Noor Khalida Inayat Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2012(2012)
• Publication Date: 2012-03-27
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2012/681348
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : 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.