Displaying similar documents to “Convexity of the inverse function”

Convex and monotone operator functions

Jaspal Singh Aujla, H. L. Vasudeva (1995)

Annales Polonici Mathematici

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The purpose of this note is to provide characterizations of operator convexity and give an alternative proof of a two-dimensional analogue of a theorem of Löwner concerning operator monotonicity.

A generalization of the Hahn-Banach theorem

Jolanta Plewnia (1993)

Annales Polonici Mathematici

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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.

Extensions of convex functionals on convex cones

E. Ignaczak, A. Paszkiewicz (1998)

Applicationes Mathematicae

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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.

Sufficient conditions for convexity in manifolds without focal points

M. Beltagy (1993)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, local, global, strongly local and strongly global supportings of subsets in a complete simply connected smooth Riemannian manifold without focal points are defined. Sufficient conditions for convexity of subsets in the same sort of manifolds have been derived in terms of the above mentioned types of supportings.

On localizing global Pareto solutions in a given convex set

Agnieszka Drwalewska, Lesław Gajek (1999)

Applicationes Mathematicae

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Sufficient conditions are given for the global Pareto solution of the multicriterial optimization problem to be in a given convex subset of the domain. In the case of maximizing real valued-functions, the conditions are sufficient and necessary without any convexity type assumptions imposed on the function. In the case of linearly scalarized vector-valued functions the conditions are sufficient and necessary provided that both the function is concave and the scalarization is increasing...