Displaying similar documents to “The polynomial hull of unions of convex sets in ℂ n ”

Hyperbolically convex functions II

William Ma, David Minda (1999)

Annales Polonici Mathematici

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Unlike those for euclidean convex functions, the known characterizations for hyperbolically convex functions usually contain terms that are not holomorphic. This makes hyperbolically convex functions much harder to investigate. We give a geometric proof of a two-variable characterization obtained by Mejia and Pommerenke. This characterization involves a function of two variables which is holomorphic in one of the two variables. Various applications of the two-variable characterization...

Convex Sets and Convex Combinations on Complex Linear Spaces

Hidenori Matsuzaki, Noboru Endou, Yasunari Shidama (2008)

Formalized Mathematics

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In this article, convex sets, convex combinations and convex hulls on complex linear spaces are introduced.MML identifier: CONVEX4, version: 7.8.10 4.99.1005

On zeros and fixed points of multifunctions with non-compact convex domains

Sehie Park, Jong Sook Bae (1993)

Commentationes Mathematicae Universitatis Carolinae

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Using our own generalization [7] of J.C. Bellenger’s theorem [1] on the existence of maximizable u.s.cq̇uasiconcave functions on convex spaces, we obtain extended versions of the existence theorem of H. Ben-El-Mechaiekh [2] on zeros for multifunctions with non-compact domains, the coincidence theorem of S.H. Kum [5] for upper hemicontinuous multifunctions, and the Ky Fan type fixed point theorems due to E. Tarafdar [13].