Abstract and Applied Analysis

Hybrid Algorithms for Solving Variational Inequalities, Variational Inclusions, Mixed Equilibria, and Fixed Point Problems

Lu-Chuan Ceng, Adrian Petrusel, Mu-Ming Wong, and Jen-Chih Yao

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Abstract

We present a hybrid iterative algorithm for finding a common element of the set of solutions of a finite family of generalized mixed equilibrium problems, the set of solutions of a finite family of variational inequalities for inverse strong monotone mappings, the set of fixed points of an infinite family of nonexpansive mappings, and the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed hybrid iterative algorithm has strong convergence under some mild conditions imposed on algorithm parameters. Here, our hybrid algorithm is based on Korpelevič’s extragradient method, hybrid steepest-descent method, and viscosity approximation method.

Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2014), Article ID 208717, 22 pages.

Dates
First available in Project Euclid: 6 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1412607614

Digital Object Identifier
doi:10.1155/2014/208717

Mathematical Reviews number (MathSciNet)
MR3176723

Zentralblatt MATH identifier
07021931

Citation

Ceng, Lu-Chuan; Petrusel, Adrian; Wong, Mu-Ming; Yao, Jen-Chih. Hybrid Algorithms for Solving Variational Inequalities, Variational Inclusions, Mixed Equilibria, and Fixed Point Problems. Abstr. Appl. Anal. 2014, Special Issue (2014), Article ID 208717, 22 pages. doi:10.1155/2014/208717. https://projecteuclid.org/euclid.aaa/1412607614


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