Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 451-462

VALUE REGIONS OF UNIVALENT SELF-MAPS WITH TWO BOUNDARY FIXED POINTS

Pavel Gumenyuk and Dmitri Prokhorov

University of Stavanger, Department of Mathematics and Natural Sciences
N-4036 Stavanger, Norway; pavel.gumenyuk 'at' uis.no

Petrozavodsk State University, Lenina 33, 185910 Petrozavodsk, Russia
and Saratov State University, Department of Mathematics and Mechanics
Astrakhanskaya 83, 410012 Saratov, Russia; ProkhorovDV 'at' info.sgu.ru

Abstract. In this paper we find the exact value region V(z₀,T) of the point evaluation functional f → f(z₀) over the class of all holomorphic injective self-maps f : D → D of the unit disk D having a boundary regular fixed point at σ = –1 with f'(–1) = e^T and the Denjoy–Wolff point at τ = 1.

2010 Mathematics Subject Classification: Primary 30C75, 30D05; Secondary 30C35, 30C55, 30C80.

Key words: Univalent function, value region, extremal problem, Denjoy–Wolff point, angular derivative, holomorphic self-map.

Reference to this article: P. Gumenyuk and D. Prokhorov: Value regions of univalent self-maps with two boundary fixed points. Ann. Acad. Sci. Fenn. Math. 43 (2018), 451-462.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4321