Abstract
The notion of a convex set is generalized. In the definition of ordinary convexity, sums of products of vectors and numbers are used. In the generalization considered in this paper, the role of numbers is played by matrices; this is why we call it “matrix convexity.”
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References
V. V. Ostapenko, “H-convex sets and integration of many-valued mappings,”Ukr. Mat. Zh.,39, No. 5, 588–592 (1987).
V. V. Ostapenko and S. N. Kalimoldaeva, “An analytic method for solution of the approach-deviation problem in a linear differential game with terminal payoff function,”Kibernetika, No. 1, 98–101 (1987).
B. N. Pshenichnyi and V. V. Ostapenko,Differential Games [in Russian], Naukova Dumka, Kiev (1992).
V. G. Boltyanskii and P. S. Soltan,Combinatorial Geometry of Various Classes of Convex Sets [in Russian], Shtiintsa, Kishinev (1978).
R. T. Rockafellar,Convex Analysis, Princeton University Press, Princeton (1970).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 64–69, January, 1995.
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Ostapenko, V.V. Matrix convexity. Ukr Math J 47, 74–80 (1995). https://doi.org/10.1007/BF01058797
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DOI: https://doi.org/10.1007/BF01058797