An extension of the class of set-valued ratios of affine functions

Author:

Orzan Alexandru1

Affiliation:

1. 1 Babeş-Bolyai University, Faculty of Mathematics and Computer Sciences , Department of Mathematics 1 , Kogălniceanu Street, 400084 Cluj-Napoca , Romania

Abstract

Abstract The aim of this paper is to generalize the convexity preserving properties of sets by direct and inverse images initially stated for set-valued ratios of affine functions to a broader class of fractional type set-valued functions which strictly includes the first one.

Publisher

Walter de Gruyter GmbH

Subject

General Medicine

Reference12 articles.

1. J. P. Aubin, H. Frankowska, Set-Valued Analysis, Birhäuser, Boston, 1990.

2. C. Berge, Topological Spaces Including a Treatment of Multi-Valued Functions, Vector Spaces and Convexity, Oliver & Boyd, Edinburgh-London, 1963.

3. A. Cambini, L. Martein, Generalized convexity and optimization: Theory and Applications, Springer-Verlag, Berlin, 2009.

4. F. Deutsch, I. Singer, On single-valuedness of convex set-valued maps, Set-Valued Anal., no. 1, 1993, 97-103.

5. A. Göpfert, H. Riahi, C. Tammer, C. Zălinescu, Variational Methods in Partially Ordered Spaces, Springer-Verlag, New York, 2003.

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