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

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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.

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Authors and Affiliations

  1. Department of Mathematics and Physics, North China Electric Power University, Baoding, 071003, China

    Shenghua Wang

  2. Dipartimento di Matematica, Universitá della Calabria, 87036, Arcavacata di Rende (CS), Italy

    Giuseppe Marino

  3. Department of Information Management, Cheng Shiu University, Kaohsiung, 833, Taiwan

    Yeong-Cheng Liou

Authors
  1. Shenghua Wang
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  2. Giuseppe Marino
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  3. Yeong-Cheng Liou
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Correspondence to Shenghua Wang.

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Wang, S., Marino, G. & Liou, YC. Strong convergence theorems for variational inequality, equilibrium and fixed point problems with applications. J Glob Optim 54, 155–171 (2012). https://doi.org/10.1007/s10898-011-9754-6

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  • DOI: https://doi.org/10.1007/s10898-011-9754-6

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