published by Tishreen University
in 2016
in Mathematics
and research's language is
العربية
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Abstract in English
The supporting functions are powerful tools for studying several problems in mathematics and engineering sciences, since they have useful advantages.
In this paper, we prove that the following conditions and statements are equivalent:
1. is convex.
2. is supporting
3. is subadditive on the unit sphere.
References used
(ROCKAFELLARR. T.Convex Analysis. Section 13, Princeton, New jersey University Press, (1970) (pp.112-127
(KRIVAN V, Technical note On the Intersection of Contingent Cones, Journal of optimization theory and applications. Vol,70,No.2, (1991
(PRINCE,J. L. and A. S. Willsky, Reconstructing Convex Sets from Support Line Measurements. Vol. 12. No. 4 ,April (1990). (pp. 377-389