Abstract
Let be such that as , let and be two positive numbers such that , and let be a contraction. If be a continuous asymptotically pseudocontractive self-mapping of a nonempty bounded closed convex subset of a real reflexive Banach space with a uniformly Gateaux differentiable norm, under suitable conditions on the sequence , we show the existence of a sequence satisfying the relation and prove that converges strongly to the fixed point of , which solves some variational inequality provided is uniformly asymptotically regular. As an application, if be an asymptotically nonexpansive self-mapping of a nonempty bounded closed convex subset of a real Banach space with a uniformly Gateaux differentiable norm and which possesses uniform normal structure, we prove that the iterative process defined by converges strongly to the fixed point of .
Citation
Xionghua Wu. Yeong-Cheng Liou. Zhitao Wu. Pei-Xia Yang. "Viscosity Methods of Asymptotically Pseudocontractive and Asymptotically Nonexpansive Mappings for Variational Inequalities." Abstr. Appl. Anal. 2012 1 - 14, 2012. https://doi.org/10.1155/2012/453452
Information