Hybrid Extragradient Methods for Finding Zeros of Accretive Operators and Solving Variational Inequality and Fixed Point Problems in Banach Spaces

Lu-Chuan Ceng and Ching-Feng Wen

Abstract and Applied Analysis, 2013, vol. 2013, 1-27

Abstract:

We introduce and analyze hybrid implicit and explicit extragradient methods for finding a zero of an accretive operator and solving a general system of variational inequalities and a fixed point problem of an infinite family of nonexpansive self-mappings in a uniformly convex Banach space which has a uniformly Gateaux differentiable norm. We establish some strong convergence theorems for hybrid implicit and explicit extra-gradient algorithms under suitable assumptions. Furthermore, we derive the strong convergence of hybrid implicit and explicit extragradient algorithms for finding a common element of the set of zeros of an accretive operator and the common fixed point set of an infinite family of nonexpansive self-mappings and a self-mapping whose complement is strictly pseudocontractive and strongly accretive in . The results presented in this paper improve, extend, supplement, and develop the corresponding results announced in the earlier and very recent literature.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:894926

DOI: 10.1155/2013/894926

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