Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)

For citation:

Gordienko V. G., Samsonova K. A. Determination of the Boundary in the Local Charzynski–Tammi Conjecture for the Fifth Coefficient. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2013, vol. 13, iss. 4, pp. 5-14. DOI: 10.18500/1816-9791-2013-13-4-5-14

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
15.12.2013
Full text:
download
(downloads: 136)
Language: 
Russian
Heading: 
Mathematics
UDC: 
517.54
DOI: 
10.18500/1816-9791-2013-13-4-5-14

Determination of the Boundary in the Local Charzynski–Tammi Conjecture for the Fifth Coefficient

Autors: 
Gordienko Valeriy Gennadievich, Saratov State University
Samsonova Kristina Aleksandrovna, Saratov State University
Abstract: 

In this article we find the exact value ofM5 such that the symmetrized Pick function PM4(z) is an extreme in the local Charzynski– Tammi conjecture for the fifth Taylor coefficient of the normalized holomorphic bounded univalent functions

Key words: 
L¨owner equation
optimum control
Pontryagin maxsimum principle
References: 
  1. Branges L. A proof of the Bieberbach conjecture. LOMI Preprints E-5-84, 1984, pp. 1–21.
  2. Branges L. A proof of the Bieberbach conjecture. Acta Math., 1985, vol. 154, no 1–2, pp. 137–152.
  3. Pick G. ¨Uber die konforme Abbildung eines Kreises auf ein schlichtes und zugleich beschr¨anktes Gebiet. S.-B. Kaiserl. Akad. Wiss. Wien. Math., Naturwiss. Kl. Abt. II a, 1917, B. 126, pp. 247–263.
  4. Schaeffer A. C., Spencer D. C. The coefficients of schlicht functions. Duke Math. J., 1945, vol. 12, pp. 107–125.
  5. Schiffer M., Tammi O. On the fourth coefficient of bounded univalent functions. Trans. Amer. Math. Soc., 1965, vol. 119, pp. 67–78. 
  6. Siewierski L. Sharp estimation of the coefficients of bounded univalent functions near the identity. Bull. Acad. Polon. Sci., 1968, vol. 16, pp. 575–576.
  7. Siewierski L. Sharp estimation of the coefficients of bounded univalent functions close to identity. Dissertationes Math. (Rozprawy Mat.), 1971, vol. 86, pp. 1–153.
  8. Schiffer M., Tammi O. On bounded univalent functions which are close to identity. Ann. Acad. Sci. Fenn. Ser. AI Math., 1968, vol. 435, pp. 3–26.
  9. Prokhorov D. V., Gordienko V. G. Definition of the boundary in the local Charzynski–Tammi conjecture. Russ. Math. (Izvestiya VUZ. Matematika), 2008, vol. 52, no. 9, pp. 51–59.
  10. Prokhorov D. V. Sets of values of systems of functionals in classes of univalent functions. Mathematics of the USSR-Sbornik, 1992, vol. 71, no. 2, pp. 499–516.
  11. Pontryagin L. S., Boltyanskii V. G., Gamkrelidze R. V., Mischenko E. F. Matematicheskaya teoriya optimal’nykh protsessov [The Mathematical Theory of Optimal Processes], Moscow, Nauka, 1969, 384 p. (in Russian).
Short text (in English):
download
(downloads: 60)
  • 849 reads