Displaying similar documents to “Some results on stability and on characterization of K-convexity of set-valued functions”

Convex Sets and Convex Combinations on Complex Linear Spaces

Hidenori Matsuzaki, Noboru Endou, Yasunari Shidama (2008)

Formalized Mathematics

Similarity:

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

Extensions of convex functionals on convex cones

E. Ignaczak, A. Paszkiewicz (1998)

Applicationes Mathematicae

Similarity:

We prove that under some topological assumptions (e.g. if M has nonempty interior in X), a convex cone M in a linear topological space X is a linear subspace if and only if each convex functional on M has a convex extension on the whole space X.

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

Sehie Park, Jong Sook Bae (1993)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

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].

Hyperbolically convex functions II

William Ma, David Minda (1999)

Annales Polonici Mathematici

Similarity:

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...

A generalization of the Hahn-Banach theorem

Jolanta Plewnia (1993)

Annales Polonici Mathematici

Similarity:

If C is a non-empty convex subset of a real linear space E, p: E → ℝ is a sublinear function and f:C → ℝ is concave and such that f ≤ p on C, then there exists a linear function g:E → ℝ such that g ≤ p on E and f ≤ g on C. In this result of Hirano, Komiya and Takahashi we replace the sublinearity of p by convexity.