Geodesic
Holomorphic mappings of the unit disc into itself with two fixed points
Sbornik. Mathematics, Tome 208 (2017) no. 3, pp. 360-376 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper is concerned with holomorphic mappings of the unit disc into itself with two fixed points. Two cases are considered: when one fixed point lies inside the disc and the other lies on the boundary and when both fixed points lie on the boundary. The effect that angular derivatives at boundary fixed points have on the properties of functions inside the unit disc is studied. Conditions on the angular derivatives to guarantee the existence of domains of univalence inside the unit disc are given. The effect of the angular derivatives on the values of the Taylor coefficients of functions is also examined. Bibliography: 19 titles.
Keywords: holomorphic mapping, fixed point, angular derivative
Mots-clés : domain of univalence, coefficient region. 
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     title = {Holomorphic mappings of the unit disc into itself with two fixed points},
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V. V. Goryainov. Holomorphic mappings of the unit disc into itself with two fixed points. Sbornik. Mathematics, Tome 208 (2017) no. 3, pp. 360-376. http://geodesic.mathdoc.fr/item/SM_2017_208_3_a3/

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