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Abstrakty
We consider a class of univalent functions which verify a strong Milin type condition for logarithmic coefficients. This class contains all alfa-Koebe spirallike functions, all extremal points of the class of typically real functions, together with their rotations and multiplicative "compositions". We find some extremal functions of this class.
Wydawca
Czasopismo
Rocznik
Tom
Strony
567--578
Opis fizyczny
Bibliogr. 19 poz.
Twórcy
autor
- Department of Mathematics, "Babes Bolyai" University, 3400 Cluj-Napoca, Romania
Bibliografia
- [1] R. Askey, G. Gasper, Positive Jacobi polynomial sums II, Amer. J. Math. 98 (1976), 709-737.
- [2] L. Bieberbach, Über die Koeffizienten derjeniken Potenzreihen, welche eine schlichte Abbildung des Einheitskreises vermitteln, S.-B Preuss. Akad. Wiss. (1916), 940-955.
- [3] The Bieberbach Conjecture, (Proceedings of the Symposium on the Occasion of the Proof), Mathematical Surveys and Monographs, 21, Amer. Math. Society 1986.
- [4] L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152.
- [5] P. L. Duren, Univalent Functions, Springer-Verlag, New York Berlin Heidelberg Tokyo 1983.
- [6] C. H. Fitzgerald, Ch. Pommerenke, The de Branges theorem on univalent functions, Trans. Amer. Math. Soc., 290, 2 (1985), 683-690.
- [7] G. Gasper, A short proof of an inequality used by de Branges in his proof of the Bieberbach, Robertson and Milin conjectures, Complex Variables Theory Appl. 7 (1986), 45-50.
- [8] S. Gong, The Bieberbach Conjecture, American Mathematical Society, Providence, RI; International Press Cambridge, Ma, 1999.
- [9] A. W. Goodman, Univalent Functions, vol. I, Mariner Publishing Company Inc, 1983.
- [10] A. Z. Grinshpan, The Bieberbach conjecture and Milin's functionals, Amer.-Math. Monthly 106 (1999) 3, 203-214.
- [11] N. D. Kazarinoff, Special functions and the Bieberbach conjecture, Amer. Math Monthly, 95 (1988), 8, 689-696.
- [12] P. P. Kufarev, On one-parameter families of analytic functions, Mat. Sb. 13 (55) (1943), 87-118. (in Russian).
- [13] P. P. Kufarev, A theorem on solutions of a differential equation, Uchen. Zap. Tomsk. Gos. Univ., 5 (1947), 20-21. (in Russian)
- [14] I. M. Milin, Univalent Functions and Orthonormal Systems, lzdat. "Nauka" , Moscow, 1971 (in Russian) .
- [15] M. S. Robertson, A remark on the odd schlicht functions, Bull. Amer. Math. Soc., 42 (1936), 366-370.
- [16] I. Şerb, Remarks on de Branges's proof of the Bieberbach conjecture (submitted).
- [17] P. G. Todorov, A simple proof of the Bieberbach Conjecture, Serdica 19 (1993) 2-3, 204-214.
- [18] P. G. Todorov, A new proof of the final stage of the proof of the Milin, Robertson and Bieberbach conjectures which does not use the Askey and Gasper inequality, Acad. Roy. Belg. Bull. Cl. Sci. (6) 9 (1998) no. 7-12, 349-359.
- [19] L. Weinstein, The Bieberbach Conjecture, Internat Math. Res. Notices (1991), 5, 61-64.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0014-0005