Geodesic
The analytic fixed point function and its properties
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 21, Tome 337 (2006), pp. 238-252

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Some properties of the analytic fixed point function, introduced recently by D. Mejia and Ch. Pommerenke, are discussed. In particular, several extremal properties of such functions, related to mappings from the unit disk onto symmetric Riemann surfaces, are established. Bibliography: 17 titles. 
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     author = {A. Yu. Solynin},
     title = {The analytic fixed point function and its properties},
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     url = {http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a13/}
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A. Yu. Solynin. The analytic fixed point function and its properties. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 21, Tome 337 (2006), pp. 238-252. http://geodesic.mathdoc.fr/item/ZNSL_2006_337_a13/