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Generalized Vector Equilibrium Problems for Pseudomonotone Multivalued Bifunctions1

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Abstract

In this paper, we apply a new version of the Brézis, Nirenberg, and Stampacchia theorem; we use pseudomonotonicity and some coercivity conditions to establish some existence result for a solution of generalized vector equilibrium problems for multivalued bifunctions. The proper quasiconvexity of multivalued bifunctions is introduced and existence theorems for generalized vector equilibrium problems related to multivalued mappings with the KKM property are obtained. The new results extend and modify various existence theorems for similar problems.

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Authors and Affiliations

  1. Assistant Professor, Department of Mathematics, University of Isfahan, Isfahan, Iran

    M. Fakhar

  2. Professor, Department of Mathematics, University of Isfahan, Isfahan, Iran

    J. Zafarani

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  1. M. Fakhar
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  2. J. Zafarani
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F. Giannessi

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Fakhar, M., Zafarani, J. Generalized Vector Equilibrium Problems for Pseudomonotone Multivalued Bifunctions1. J Optim Theory Appl 126, 109–124 (2005). https://doi.org/10.1007/s10957-005-2663-4

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