Convergence of Paths for Perturbed Maximal Monotone Mappings in Hilbert Spaces. (5th January 2011)

• Record Type: Journal Article
• Authors: Qing, Yuan; Qin, Xiaolong; Zhou, Haiyun; Kang, Shin Min
• Other Names: Ciric Ljubomir B. Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2010(2010)
• Publication Date: 2011-01-05
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2010/547828
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : LetH be a Hilbert space andC a nonempty closed convex subset ofH . LetA : C → H be a maximal monotone mapping andf : C → C a bounded demicontinuous strong pseudocontraction. Let{ x t } be the unique solution to the equationf ( x ) = x + t A x . Then{ x t } is bounded if and only if{ x t } converges strongly to a zero point of A ast → ∞ which is the unique solution inA − 1 ( 0 ), whereA − 1 ( 0 ) denotes the zero set ofA, to the following variational inequality〈 f ( p ) − p, y − p 〉 ≤ 0, for ally ∈ A − 1 ( 0 ) .