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AMBIENTUM BIOETHICA BIOLOGIA CHEMIA DIGITALIA DRAMATICA EDUCATIO ARTIS GYMNAST. ENGINEERING EPHEMERIDES EUROPAEA GEOGRAPHIA GEOLOGIA HISTORIA HISTORIA ARTIUM INFORMATICA IURISPRUDENTIA MATHEMATICA MUSICA NEGOTIA OECONOMICA PHILOLOGIA PHILOSOPHIA PHYSICA POLITICA PSYCHOLOGIA-PAEDAGOGIA SOCIOLOGIA THEOLOGIA CATHOLICA THEOLOGIA CATHOLICA LATIN THEOLOGIA GR.-CATH. VARAD THEOLOGIA ORTHODOXA THEOLOGIA REF. TRANSYLVAN
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STUDIA MATHEMATICA - Issue no. 3 / 2021 | |||||||
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CONVEXITY-PRESERVING PROPERTIES OF SET-VALUED RATIOS OF AFFINE FUNCTIONS. Authors: ALEXANDRU ORZAN, NICOLAE POPOVICI. |
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Abstract: DOI: 10.24193/subbmath. 2021.3.14 Published Online: 2021-09-30 Published Print: 2021-09-30 pp. 591-602 VIEW PDF FULL PDF The aim of this paper is to introduce some classes of set-valued functions that preserve the convexity of sets by direct and inverse images. In particular, we show that the so-called set-valued ratios of affine functions represent such a class. To this aim, we characterize them in terms of vector-valued selections that are ratios of affine functions in the classical sense of Rothblum. Mathematics Subject Classification (2010): 54C60, 26B25. Keywords: Set-valued affine function, single-valued selection, ratio of affine functions, generalized convexity. |
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