Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2012, Special Issue (2012), Article ID 414831, 35 pages.

A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings

Poom Kumam and Phayap Katchang

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Abstract

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (2010) and many others.

Article information

Source
J. Appl. Math., Volume 2012, Special Issue (2012), Article ID 414831, 35 pages.

Dates
First available in Project Euclid: 3 January 2013

Permanent link to this document
https://projecteuclid.org/euclid.jam/1357180292

Digital Object Identifier
doi:10.1155/2012/414831

Mathematical Reviews number (MathSciNet)
MR2915729

Zentralblatt MATH identifier
1245.49014

Citation

Kumam, Poom; Katchang, Phayap. A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings. J. Appl. Math. 2012, Special Issue (2012), Article ID 414831, 35 pages. doi:10.1155/2012/414831. https://projecteuclid.org/euclid.jam/1357180292


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