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Generalizations of vector quasivariational inclusion problems with set-valued maps

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Abstract

Existence theorems are given for the problem of finding a point (z 0,x 0) of a set E × K such that \((z_0,x_0)\in B(z_0,x_0)\times A(z_0,x_0)\) and, for all \(\eta\in A(z_0,x_0), (F(z_0,x_0,x_0,\eta), C(z_0,x_0,x_0,\eta))\in \alpha\) where α is a relation on 2Y (i.e., a subset of 2Y × 2Y), \(A : E\times K\longrightarrow 2^K,\) \(B : E\times K\longrightarrow 2^E, C : E\times K\times K\times K\longrightarrow 2^Y\) and \(F : E\times K\times K\times K\longrightarrow 2^Y\) are some set-valued maps, and Y is a topological vector space. Detailed discussions are devoted to special cases of α and C which correspond to several generalized vector quasi-equilibrium problems with set-valued maps. In such special cases, existence theorems are obtained with or without pseudomonotonicity assumptions.

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Authors and Affiliations

  1. Hanoi Institute of Mathematics, 18 Hoang Quoc Viet Road, 10307, Hanoi, Vietnam

    Pham Huu Sach

  2. Ninh Thuan College of Pedagogy, Ninh Thuan, Vietnam

    Le Anh Tuan

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  1. Pham Huu Sach
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  2. Le Anh Tuan
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Correspondence to Pham Huu Sach.

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Sach, P.H., Tuan, L.A. Generalizations of vector quasivariational inclusion problems with set-valued maps. J Glob Optim 43, 23–45 (2009). https://doi.org/10.1007/s10898-008-9289-7

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  • DOI: https://doi.org/10.1007/s10898-008-9289-7

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