Continuity of approximate solution maps to vector equilibrium problems Article Swipe

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Hausdorff space Vector optimization Variational inequality Mathematics Locally convex topological vector space Applied mathematics Parametric statistics Dual (grammatical number) Mathematical optimization Hausdorff distance Regular polygon Dual space Computer science Optimization problem Mathematical analysis Pure mathematics Multi-swarm optimization Art Literature Geometry Statistics

Lâm Quốc Anh , Pham Thanh Duoc , Tran Ngoc Tam ·

YOU? · · 2016 · Open Access · · DOI: https://doi.org/10.3934/jimo.2017013 · OA: W2560102486

This paper considers the parametric primal and dual vector equilibrium problems in locally convex Hausdorff topological vector spaces. Based on linear scalarization technique, we establish sufficient conditions for the continuity of approximate solution maps to these problems. As applications, some new results for vector optimization problem and vector variational inequality are derived. Our results are new and improve the existing ones in the literature.