Abstract and Applied Analysis

A Viscosity Hybrid Steepest Descent Method for Generalized Mixed Equilibrium Problems and Variational Inequalities for Relaxed Cocoercive Mapping in Hilbert Spaces

Wanpen Chantarangsi, Chaichana Jaiboon, and Poom Kumam

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Abstract

We present an iterative method for fixed point problems, generalized mixed equilibrium problems, and variational inequality problems. Our method is based on the so-called viscosity hybrid steepest descent method. Using this method, we can find the common element of the set of fixed points of a nonexpansive mapping, the set of solutions of generalized mixed equilibrium problems, and the set of solutions of variational inequality problems for a relaxed cocoercive mapping in a real Hilbert space. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality. The results presented in this paper generalize and extend some well-known strong convergence theorems in the literature.

Article information

Source
Abstr. Appl. Anal., Volume 2010 (2010), Article ID 390972, 39 pages.

Dates
First available in Project Euclid: 1 November 2010

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1288620741

Digital Object Identifier
doi:10.1155/2010/390972

Mathematical Reviews number (MathSciNet)
MR2669084

Zentralblatt MATH identifier
1206.47067

Citation

Chantarangsi, Wanpen; Jaiboon, Chaichana; Kumam, Poom. A Viscosity Hybrid Steepest Descent Method for Generalized Mixed Equilibrium Problems and Variational Inequalities for Relaxed Cocoercive Mapping in Hilbert Spaces. Abstr. Appl. Anal. 2010 (2010), Article ID 390972, 39 pages. doi:10.1155/2010/390972. https://projecteuclid.org/euclid.aaa/1288620741


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