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Generalized Convex Envelopes of Sets and the Problem of Shadow

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Abstract

The principal goal of the present work is to solve the problem of shadow for any convex set with nonempty interior in the n-dimensional Euclidean space and under the action of a group of transformations. This problem can be considered as the determination of conditions ensuring the membership of a point to a generalized convex envelope of the family of sets obtained from the initial set by the action of the group of transformations.

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Authors and Affiliations

  1. Institute of Mathematics of the NAS of Ukraine, Kiev, Ukraine

    Yurii B. Zelinskii

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  1. Yurii B. Zelinskii
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Correspondence to Yurii B. Zelinskii.

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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 12, No. 2, pp. 278–289, April–May, 2015.

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Zelinskii, Y.B. Generalized Convex Envelopes of Sets and the Problem of Shadow. J Math Sci 211, 710–717 (2015). https://doi.org/10.1007/s10958-015-2626-8

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  • DOI: https://doi.org/10.1007/s10958-015-2626-8

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