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Strong convergence theorems for variational inequality, equilibrium and fixed point problems with applications

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  • Shenghua Wang
  • Giuseppe Marino
  • Yeong-Cheng Liou

Abstract

In this paper, we introduce a new iterative scheme for finding a common element of the set of common solutions of a finite family of equilibrium problems with relaxed monotone mappings, of the set of common solutions of a finite family of variational inequalities and of the set of common fixed points of an infinite family of nonexpansive mappings in a Hilbert space. Strong convergence for the proposed iterative scheme is proved. As an application, we solve a multi-objective optimization problem using the result of this paper. Our results improve and extend the corresponding ones announced by others. Copyright Springer Science+Business Media, LLC. 2012

Suggested Citation

  • Shenghua Wang & Giuseppe Marino & Yeong-Cheng Liou, 2012. "Strong convergence theorems for variational inequality, equilibrium and fixed point problems with applications," Journal of Global Optimization, Springer, vol. 54(1), pages 155-171, September.
    • Handle: RePEc:spr:jglopt:v:54:y:2012:i:1:p:155-171
    DOI: 10.1007/s10898-011-9754-6
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    References listed on IDEAS

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    1. L. C. Ceng & A. Petruşel & J. C. Yao, 2009. "Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 37-58, October.
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