We shall be concerned in this paper with an optimization problem of the form: J(f) → min(max) subject to f ∈ 𝓕 where 𝓕 is some family of complex functions that are analytic in the unit disc. For this problem, the question about its characteristic properties is considered. The possibilities of applications of the results of general optimization theory to such a problem are also examined.
@article{bwmeta1.element.bwnjournal-article-bcpv31z1p61bwm,
author = {Baranowicz, J\'ozef and Miko\l ajczyk, Leon},
title = {On the characteristic properties of certain optimization problems in complex analysis},
journal = {Banach Center Publications},
volume = {31},
year = {1995},
pages = {61-67},
zbl = {0844.49019},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p61bwm}
}
Baranowicz, Józef; Mikołajczyk, Leon. On the characteristic properties of certain optimization problems in complex analysis. Banach Center Publications, Tome 31 (1995) pp. 61-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-bcpv31z1p61bwm/
[000] [1] J. Baranowicz and M. Studniarski, A locally convex extremal problem over some family of complex functions, Math. Nachr. 146 (1990), 117-125. | Zbl 0713.49033
[001] [2] J. Baranowicz and S. Walczak, On some mathematical programming problem in a locally convex space, Bull. Soc. Sci. Lettres de Łódź 36 (25) (1986), 1-11. | Zbl 0612.90103
[002] [3] J. Baranowicz and S. Walczak, Necessary conditions for the existence of a solution of some extremal problems in the families of holomorphic functions, Demonstratio Math. 23 (1990), 139-154. | Zbl 0735.30027
[003] [4] L. Brickman, T. H. Mac Gregor and D. R. Wiken, Convex hulls of some classical families of univalent functions, Trans. Amer. Math. Soc. 156 (1971), 91-107.
[004] [5] D. J. Hallenbeck and T. H. Mac Gregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Pitman, 1984.
[005] [6] A. D. Joffe and V. M. Tikhomirov, Theory of Extremal Problems, Nauka, Moscow 1974 (in Russian); English transl.: North-Holland, Amsterdam 1971.
[006] [7] D. H. Luecking and L. A. Rubel, Complex Analysis--% a Functional Analysis Approach, Springer, New York, 1984. | Zbl 0546.30002
[007] [8] L. Mikołajczyk, A theorem on distorsion for univalent p-symmetrical functions bounded in the circle |z| < 1, Comment. Math. Prace Mat. 12 (1968), 35-51. | Zbl 0237.30020
[008] [9] L. Mikołajczyk and S. Walczak, Application of the extremum principle to investigating certain extremal problems, Trans. Amer. Math. Soc. 259 (1980), 147-155. | Zbl 0435.49015
[009] [10] L. Mikołajczyk and S. Walczak, On application of the Dubovitskiĭ-Milyutin method to investigating certain extremal problems, Demonstratio Math. 13 (1980), 509-530. | Zbl 0451.30033
[010] [11] Ch. Pommerenke, Univalent Functions, Göttingen, 1975.
[011] [12] M. Studniarski, Application of the Dubovitskiĭ-Milyutin method to some locally convex extremal problems, Bull. Soc. Sci. Lettres de Łódź 29 (6) (1979), 1-8.