Abstract:
In the class of holomorphic functions that mapping the unit disc into itself and having an inner and two boundary fixed points, the exact set of the values of derivative at zero in terms of the angular derivatives at the boundary fixed points is given. As a corollary in the class of such functions a disc of univalence with center at zero is found.
Keywords:
holomorphic mapping, fixed point, angular derivative, Schwarz inequality, domain of univalence.
Citation:
O. S. Kudryavtseva, “Inequality of Schwarz type for holomorphic self-maps of a disc with fixed points”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 7, 43–51; Russian Math. (Iz. VUZ), 65:7 (2021), 35–42
\Bibitem{Kud21}
\by O.~S.~Kudryavtseva
\paper Inequality of Schwarz type for holomorphic self-maps of a disc with fixed points
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2021
\issue 7
\pages 43--51
\mathnet{http://mi.mathnet.ru/ivm9694}
\crossref{https://doi.org/10.26907/0021-3446-2021-7-43-51}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2021
\vol 65
\issue 7
\pages 35--42
\crossref{https://doi.org/10.3103/S1066369X21070057}
Linking options:
https://www.mathnet.ru/eng/ivm9694
https://www.mathnet.ru/eng/ivm/y2021/i7/p43
This publication is cited in the following 2 articles:
O. S. Kudryavtseva, “Tochnye oblasti vzaimnogo izmeneniya koeffitsientov golomorfnykh otobrazhenii kruga v sebya s nepodvizhnymi tochkami”, Izv. vuzov. Matem., 2023, no. 5, 48–57
O. S. Kudryavtseva, “Exact Regions of Mutual Variation of Coefficients of Holomorphic Self-Maps of a Disc with Fixed Points”, Russ Math., 67:5 (2023), 41
Citation in format AMSBIB
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