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1995 | 31 | 1 | 61-67
Tytuł artykułu

On the characteristic properties of certain optimization problems in complex analysis

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
31
Numer
1
Strony
61-67
Opis fizyczny
Daty
wydano
1995
Twórcy
  • Institute of Mathematics, Łódź University, ul. Stefana Banacha 22, 90-238 Łódź, Poland
  • Institute of Mathematics, Łódź University, ul. Stefana Banacha 22, 90-238 Łódź, Poland
Bibliografia
  • [1] J. Baranowicz and M. Studniarski, A locally convex extremal problem over some family of complex functions, Math. Nachr. 146 (1990), 117-125.
  • [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.
  • [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.
  • [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.
  • [5] D. J. Hallenbeck and T. H. Mac Gregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Pitman, 1984.
  • [6] A. D. Joffe and V. M. Tikhomirov, Theory of Extremal Problems, Nauka, Moscow 1974 (in Russian); English transl.: North-Holland, Amsterdam 1971.
  • [7] D. H. Luecking and L. A. Rubel, Complex Analysis--% a Functional Analysis Approach, Springer, New York, 1984.
  • [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.
  • [9] L. Mikołajczyk and S. Walczak, Application of the extremum principle to investigating certain extremal problems, Trans. Amer. Math. Soc. 259 (1980), 147-155.
  • [10] L. Mikołajczyk and S. Walczak, On application of the Dubovitskiĭ-Milyutin method to investigating certain extremal problems, Demonstratio Math. 13 (1980), 509-530.
  • [11] Ch. Pommerenke, Univalent Functions, Göttingen, 1975.
  • [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.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv31z1p61bwm
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