Displaying similar documents to “An extension of Witzgall's result on convex metrics.”

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...

Minimax theorems with applications to convex metric spaces

Jürgen Kindler (1995)

Colloquium Mathematicae

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A minimax theorem is proved which contains a recent result of Pinelis and a version of the classical minimax theorem of Ky Fan as special cases. Some applications to the theory of convex metric spaces (farthest points, rendez-vous value) are presented.

On metric products

Irmina Herburt, Maria Moszyńska (1991)

Colloquium Mathematicae

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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.