Degree of Convergence of Iterative Algorithms for Boundedly Lipschitzian Strong Pseudocontractions. (29th December 2010)

• Record Type: Journal Article
• Authors: He, Songnian; Su, Yongfu; Li, Ronghua
• Other Names: Saejung Satit Academic Editor.
• Is Part Of: Fixed point theory and applications. Volume 2010(2010)
• Publication Date: 2010-12-29
• Subjects: Fixed point theory -- Periodicals; Mappings (Mathematics) -- Periodicals; 515.7248
• DOI: 10.1155/2010/210340
• Languages: English
• ISSNs: 1687-1812

Abstract

Abstract : LetC be a nonempty closed convex subset of a real Hilbert spaceH, and letT : C → H be a boundedly Lipschitzian strong pseudo-contraction with a nonempty fixed point set. Three iterative algorithms are proposed for approximating the unique fixed point ofT ; one of them is for the self-mapping case, and the others are for the nonself-mapping case. Not only the strong convergence, but also the degree of convergence of the three iterative algorithms is obtained. Some numerical results corresponding to the self-mapping case are given which show advantages of our methods. As an application of our results, adopting the regularization idea, we also propose implicit and explicit algorithms for approximating a fixed point of a boundedly Lipschitzian pseudocontractive self-mapping fromC into itself, respectively.