On a new proof and an extension of Jack’s lemma

• Autorzy: Fournier R.

Identyfikatory

DOI

10.1515/jaa-2017-0003

• Języki publikacji: EN

Abstrakty

EN

We give a new proof and discuss an extension of Jack’s lemma for polynomials.

Słowa kluczowe

EN

Jack's lemma; polynomials

PL

lemat Jacka; wielomiany

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2017
• Tom: Vol. 23, nr 1
• Strony: 21--24
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Fournier R.

• CRM and DMS, Université de Montréal, C.P. 6128, Succ. Centre-ville, Montréal, H3C 3J7, Canada

Bibliografia

• [1] J. Bak and D. J. Newman, Complex Analysis, 2nd ed., Springer, New York, 1997.
• [2] H. P. Boas, Julius and Julia: Mastering the Art of the Schwarz Lemma, Amer. Math. Monthly 117 (2010), 770-785.
• [3] L. Brickman, T. H. Macgregor and D. R. Wilken, Convex hulls of some classical families of univalent functions, Trans. Amer. Math. Soc. 156 (1971), 91-107.
• [4] D. M. Burns and S. G. Krantz, Rigidity of holomorphic mappings and a new Schwarz lemma at the boundary, J. Amer. Math. Soc. 7 (1994), 661-676.
• [5] R. Fournier, Some remarks on Jack’s lemma, Mathematica 43 (2001), 43-50.
• [6] R. Fournier, Bound-preserving operators and the maximum modulus of extremal polynomials, Comput. Methods Funct. Theory 14 (2014), 735-741.
• [7] R. Fournier and S. Ruscheweyh, On two inequalities for polynomials in the unit disk, in: Progress in Approximation Theory and Applicable Complex Analysis, Springer Optim. Appl. 117, Springer, Cam (2017), 75-82.
• [8] R. Fournier and M. Serban, An extension of Jack’s lemma to polynomials of fixed degree, Comput. Methods Funct. Theory 7 (2007), 371-378.
• [9] A. Frolova, M. Levenshtein, D. Shoikhet and A. Vasiliev, Boundary distortion estimates for holomorphic maps, Complex Anal. Oper. Theory 8 (2014), 1129-1149.
• [10] I. S. Jack, Functions starlike and convex or order , J. Lond. Math. Soc. (2) 3 (1971), 469-474.
• [11] K. Löwner, Untersuchungen über schlichte konforme Abbildungen des Einheitskreises, Math. Ann. 89 (1923), 103-121.
• [12] S. Miller and P. Mocanu, Differential Subordinations, Marcel Dekker, New York, 2000.
• [13] R. Osserman, A sharp Schwarz inequality on the boundary, Proc. Amer. Math. Soc. 128 (2000), 3513-3517.
• [14] S. Ruscheweyh, Convolutions in Geometric Function Theory, Université de Montréal, Montréal, 1982.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).