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A monotone path-connected set with outer radially lower continuous metric projection is a strict sun

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Abstract

A monotone path-connected set is known to be a sun in a finite-dimensional Banach space. We show that a B-sun (a set whose intersection with each closed ball is a sun or empty) is a sun. We prove that in this event a B-sun with ORL-continuous (outer radially lower continuous) metric projection is a strict sun. This partially converses one well-known result of Brosowski and Deutsch. We also show that a B-solar LG-set (a global minimizer) is a B-connected strict sun.

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References

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    A. R. Alimov

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  1. A. R. Alimov
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Correspondence to A. R. Alimov.

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Moscow. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 58, No. 1, pp. 16–21, January–February, 2017; DOI: 10.17377/smzh.2017.58.102.

The author was supported by the Russian Foundation for Basic Research (Grant 16–01–00295).

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Alimov, A.R. A monotone path-connected set with outer radially lower continuous metric projection is a strict sun. Sib Math J 58, 11–15 (2017). https://doi.org/10.1134/S0037446617010025

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  • DOI: https://doi.org/10.1134/S0037446617010025

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