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Displaying similar documents to “Totally convex algebras”

Representation theorem for convex effect algebras

Stanley P. Gudder, Sylvia Pulmannová (1998)

Commentationes Mathematicae Universitatis Carolinae

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Effect algebras have important applications in the foundations of quantum mechanics and in fuzzy probability theory. An effect algebra that possesses a convex structure is called a convex effect algebra. Our main result shows that any convex effect algebra admits a representation as a generating initial interval of an ordered linear space. This result is analogous to a classical representation theorem for convex structures due to M.H. Stone.

Plurisubharmonic saddles

Siegfried Momm (1996)

Annales Polonici Mathematici

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A certain linear growth of the pluricomplex Green function of a bounded convex domain of ℂ N at a given boundary point is related to the existence of a certain plurisubharmonic function called a “plurisubharmonic saddle”. In view of classical results on the existence of angular derivatives of conformal mappings, for the case of a single complex variable, this allows us to deduce a criterion for the existence of subharmonic saddles.

Necessary and sufficient conditions for generalized convexity

Janusz Krzyszkowski (1995)

Annales Polonici Mathematici

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We give some necessary and sufficient conditions for an n-1 times differentiable function to be a generalized convex function with respect to an unrestricted n-parameter family.

Subadditive functions and partial converses of Minkowski's and Mulholland's inequalities

J. Matkowski, T. Świątkowski (1993)

Fundamenta Mathematicae

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Let ϕ be an arbitrary bijection of ℝ + . We prove that if the two-place function ϕ - 1 [ ϕ ( s ) + ϕ ( t ) ] is subadditive in ℝ + 2 then ϕ must be a convex homeomorphism of ℝ + . This is a partial converse of Mulholland’s inequality. Some new properties of subadditive bijections of ℝ + are also given. We apply the above results to obtain several converses of Minkowski’s inequality.