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Mixed equilibrium problems with Z*-bifunctions and least element problems in Banach lattices

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Abstract

The purpose of this paper is to study the relations among a mixed equilibrium problem, a least element problem and a minimization problem in Banach lattices. We propose the concept of Z*-bifunctions as well as the concept of a feasible set for the mixed equilibrium problem. We prove that the feasible set of the mixed equilibrium problem is a sublattice provided that the associated bifunction is a strictly α-monotone Z*-bifunction. We establish the equivalence of the mixed equilibrium problem, the least element problem and the minimization problem under strict α-monotonicity and Z*-bifunction conditions.

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Authors and Affiliations

  1. Department of Mathematics, Chengdu University of Information Technology, Chengdu, Sichuan, People’s Republic of China

    Rong Hu

  2. Department of Mathematics, Sichuan University, Chengdu, Sichuan, People’s Republic of China

    Ya Ping Fang

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  1. Rong Hu
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  2. Ya Ping Fang
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Correspondence to Ya Ping Fang.

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Hu, R., Fang, Y.P. Mixed equilibrium problems with Z*-bifunctions and least element problems in Banach lattices. Optim Lett 7, 933–947 (2013). https://doi.org/10.1007/s11590-012-0473-9

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