Geodesic
Inequality of Schwarz type for holomorphic self-maps of a disc with fixed points
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2021), pp. 43-51

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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
Mots-clés : domain of univalence. 
@article{IVM_2021_7_a4,
     author = {O. S. Kudryavtseva},
     title = {Inequality of {Schwarz} type for holomorphic self-maps of a disc with fixed points},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {43--51},
     publisher = {mathdoc},
     number = {7},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2021_7_a4/}
}
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O. S. Kudryavtseva. Inequality of Schwarz type for holomorphic self-maps of a disc with fixed points. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 7 (2021), pp. 43-51. http://geodesic.mathdoc.fr/item/IVM_2021_7_a4/