On the continuity of midpoint hull convex set-valued functions |
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Authors: | Antonella Fiacca Francesca Papalini |
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Affiliation: | (1) Dipartimento di Matematica, dell' Università, Via Vanvitelli 1, E-06100 Perugia, Italy |
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Abstract: | Summary The concept of hull convexity (midpoint hull convexity) for set-valued functions in vector spaces is examined. This concept, introduced by A. V. Fiacco and J. Kyparisis (Journal of Optimization Theory and Applications,43 (1986), 95–126), is weaker than one of convexity (midpoint convexity).The main result is a sufficient condition for a midpoint hull convex set-valued function to be continuous. This theorem improves a result obtained by K. Nikodem (Bulletin of the Polish Academy of Sciences, Mathematics,34 (1986), 393–399). |
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Keywords: | Primary 26E25, 26A51, 46A55 Secondary 26B25, 90C25, 54C60 |
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