Degree of Convergence of Iterative Algorithms for Boundedly Lipschitzian Strong Pseudocontractions
Songnian He, Yongfu Su, Rong-Hua Li · Fixed Point Theory and Applications · 2010
Abstract Let "Equation missing" be a nonempty closed convex subset of a real Hilbert space "Equation missing" and let "Equation missing" be a boundedly Lipschitzian strong pseudo-contraction with a nonempty fixed point set. Three iterative algorithms are proposed for approximating the unique fixed point of "Equation missing"; 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 from "Equation missing" into itself, respectively.