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Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems

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Central European Journal of Mathematics

Abstract

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem, the set of fixed points of a nonexpansive mapping, and the the set of solutions of a variational inclusion in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of a certain optimization problem related to a strongly positive bounded linear operator.

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Authors and Affiliations

  1. Department of Mathematics, Tianjin Polytechnic University, Tianjin, China

    Yonghong Yao

  2. Department of Mathematics Education and RINS, Gyeongsang National University, Chinju, Korea

    Yeol Je Cho

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

    Yeong-Cheng Liou

Authors
  1. Yonghong Yao
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  2. Yeol Je Cho
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  3. Yeong-Cheng Liou
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Correspondence to Yonghong Yao.

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Yao, Y., Cho, Y.J. & Liou, YC. Iterative algorithms for variational inclusions, mixed equilibrium and fixed point problems with application to optimization problems. centr.eur.j.math. 9, 640–656 (2011). https://doi.org/10.2478/s11533-011-0021-3

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  • DOI: https://doi.org/10.2478/s11533-011-0021-3

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