On the characteristic properties of certain optimization problems in complex analysis

Józef Baranowicz; Leon Mikołajczyk

Banach Center Publications (1995)

  • Volume: 31, Issue: 1, page 61-67
  • ISSN: 0137-6934

Abstract

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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.

How to cite

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Baranowicz, Józef, and Mikołajczyk, Leon. "On the characteristic properties of certain optimization problems in complex analysis." Banach Center Publications 31.1 (1995): 61-67. <http://eudml.org/doc/262605>.

@article{Baranowicz1995,
abstract = {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.},
author = {Baranowicz, Józef, Mikołajczyk, Leon},
journal = {Banach Center Publications},
keywords = {optimization; complex functions that are analytic in the unit disc; univalent functions},
language = {eng},
number = {1},
pages = {61-67},
title = {On the characteristic properties of certain optimization problems in complex analysis},
url = {http://eudml.org/doc/262605},
volume = {31},
year = {1995},
}

TY - JOUR
AU - Baranowicz, Józef
AU - Mikołajczyk, Leon
TI - On the characteristic properties of certain optimization problems in complex analysis
JO - Banach Center Publications
PY - 1995
VL - 31
IS - 1
SP - 61
EP - 67
AB - 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.
LA - eng
KW - optimization; complex functions that are analytic in the unit disc; univalent functions
UR - http://eudml.org/doc/262605
ER -

References

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  1. [1] J. Baranowicz and M. Studniarski, A locally convex extremal problem over some family of complex functions, Math. Nachr. 146 (1990), 117-125. Zbl0713.49033
  2. [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. Zbl0612.90103
  3. [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. Zbl0735.30027
  4. [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. [5] D. J. Hallenbeck and T. H. Mac Gregor, Linear Problems and Convexity Techniques in Geometric Function Theory, Pitman, 1984. 
  6. [6] A. D. Joffe and V. M. Tikhomirov, Theory of Extremal Problems, Nauka, Moscow 1974 (in Russian); English transl.: North-Holland, Amsterdam 1971. 
  7. [7] D. H. Luecking and L. A. Rubel, Complex Analysis--% a Functional Analysis Approach, Springer, New York, 1984. Zbl0546.30002
  8. [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. Zbl0237.30020
  9. [9] L. Mikołajczyk and S. Walczak, Application of the extremum principle to investigating certain extremal problems, Trans. Amer. Math. Soc. 259 (1980), 147-155. Zbl0435.49015
  10. [10] L. Mikołajczyk and S. Walczak, On application of the Dubovitskiĭ-Milyutin method to investigating certain extremal problems, Demonstratio Math. 13 (1980), 509-530. Zbl0451.30033
  11. [11] Ch. Pommerenke, Univalent Functions, Göttingen, 1975. 
  12. [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. 

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