A Description Method in the Value Region Problem

Dmitri Prokhorov1, К. А. Самсонова1
1Saratov State University

Tóm tắt

Từ khóa


Tài liệu tham khảo

Bracci, F., Contreras, M.D., Díaz-Madrigal, S., Vasil’ev, A.: Classical and stochastic Löwner–Kufarev equations. In: Vasil’ev, A. (ed.) Harmonic and Complex Analysis and its Applications. Trends of Mathematics, pp. 39–134. Springer, Heidelberg (2014)

Fedorov, S.I.: The moduli of certain families of curves and the range of $$\{f(\zeta _0)\}$$ { f ( ζ 0 ) } in the class of univalent functions with real coefficients. Zap. Nauchn. Semin. LOMI. 139, 156-167 (1984) (English translation: Journal of Soviet Mathematics. 36, 282-291 (1987))

Goryainov, V.V., Gutlyanski, V.Ja.: On extremal problem in the class $$S_M$$ S M . Mat. Sb. Kiev 242–246 (1976)

Grunsky, H.: Neue Abschätzungen zur konformen Abbildung ein-und mehrfach zusammenhängender Bereiche. Schr. Math. Inst. u. Inst. Angew. Math. Univ. Berlin. 1, 95–140 (1932)

Jenkins, J.A.: On univalent functions with real coefficients. Ann. Math. 71, 1–15 (1960)

Prokhorov, D.: Sets of values of systems of functionals in classes of univalent functions. Mat. Sbornik. 181, 1659-1677 (1990) (English translation: Math USSR Sbornik. 71, 499–516 (1992))

Prokhorov, D.V.: Reachable Set Methods in Extremal Problems for Univalent Functions. Saratov Univ, Saratov (1993)

Prokhorov, D., Samsonova, K.: Value range of solutions to the chordal Loewner equation. J. Math. Anal. Appl. 428, 910–919 (2015)

Rogosinski, W.: Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen. Math. Z. 35, 93–121 (1932)

Rogosinski, W.: Zum Schwarzen Lemma. J. ber. Deutsche Math.-Verein 44, 258–261 (1934)

Roth, O., Schleissinger, S.: Rogosinski’s lemma for univalent functions, hyperbolic Archimedean spirals and the Loewner equation. Bull. Lond. Math. Soc. 46, 1099–1109 (2014)

Tammi, O.: Extremum Problems for Bounded Univalent Functions. Lecture Notes in Mathematics, vol. 646. Springer, Berlin-Heidelberg-New York (1978)