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