Acta Mathematica Vietnamica
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ON THE CONTINUITY OF VECTOR CONVEX MULTIVALUED FUNCTIONS
NGUYEN BA MINH, NGUYEN XUAN TANpp. 13-25
Abstract
The well-known Banach Steinhaus Theorem is extended to the case of convex and concave functions and its applications are shown to find necessary and sufficient conditions for the $C$-continuity of vector convex functions. Relations between upper and lower $C$-continuities are also obtained.