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Vector Equilibrium Problems, Minimal Element Problems and Least Element Problems

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Abstract

In this paper we introduce some concepts of feasible sets for vector equilibrium problems and some classes of Z-maps for vectorial bifunctions. Under strict pseudomonotonicity assumptions, we investigate the relationship between minimal element problems of feasible sets and vector equilibrium problems. By using Z-maps, we further study the least element problems of feasible sets for vector equilibrium problems. Finally, we prove a generalized sublattice property of feasible sets for vector equilibrium problems associated with Z-maps.

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Authors and Affiliations

  1. Department of Mathematics, Sichuan University, Chengdu Sichuan, P.R. China

    Ya-ping Fang

  2. Department of Mathematics, Sichuan University, Chengdu Sichuan, P.R. China

    Nan-jing Huang

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  1. Ya-ping Fang
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  2. Nan-jing Huang
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Correspondence to Ya-ping Fang.

Additional information

This work was supported by the National Natural Science Foundation of China and the Applied Research Project of Sichuan Province (05JY029-009-1). The authors thank Professor Charalambos D. Aliprantis and the referees for valuable comments and suggestions leading to improvements of this paper.

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Fang, Yp., Huang, Nj. Vector Equilibrium Problems, Minimal Element Problems and Least Element Problems. Positivity 11, 251–268 (2007). https://doi.org/10.1007/s11117-006-2034-x

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  • DOI: https://doi.org/10.1007/s11117-006-2034-x

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