Semi-algebraic Semicontinuity Of Vector-valued Maps And Applications
Keywords:
Semicontinuity, algebraic interior, vector equilibrium problem, existence of solution, generalized quasiconvexity.Abstract
T
his paper proposes concepts of semicontinuity of vector-valued maps in the sense of “semi-algebra”, that is, the image spaces are not endowed with any particular topology. Properties as well as characterizations of these concepts are discussed. We use these results together with new concepts of generalized quasiconvexity of vector-valued map to study existence conditions and the (semi)continuity of solution maps to vector equilibrium problems. Wellposedness under perturbations for vector equilibrium problems with equilib
rium constraints is also presented.
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