Geodesic
The region of values of the system $\{f(z_1),f(z_2),f(z_3)\}$ on the class of typically real functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 19, Tome 302 (2003), pp. 5-17 Cet article a éte moissonné depuis la source Math-Net.Ru

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The paper determines the region of values of the system occurring in the title on the class $T$ of functions $f(z)=z+\dotsb$ regular in the unit disk and satisfying the condition $\operatorname{Im}f(z)\cdot\operatorname{Im}z>0$ for $\operatorname{Im}z\ne0$. 
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E. G. Goluzina. The region of values of the system $\{f(z_1),f(z_2),f(z_3)\}$ on the class of typically real functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 19, Tome 302 (2003), pp. 5-17. http://geodesic.mathdoc.fr/item/ZNSL_2003_302_a0/

[1] W. Rogosinski, “Über positive harmonische Entwicklungen und typisch-reelle Potenzreihen”, Math. Z, 35:1 (1932), 93–121 | DOI | MR

[2] E. G. Goluzina, “Ob oblastyakh znachenii nekotorykh sistem funktsionalov v klasse tipichno veschestvennykh funktsii”, Vestn. LGU, ser. mat., mekh., i astr., 7:2 (1965), 45–63 | MR

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