Geodesic
Distortion theorems for circumferentially mean $p$-valent functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 43-56 
V. N. Dubinin. Distortion theorems for circumferentially mean $p$-valent functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 30, Tome 440 (2015), pp. 43-56. http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a3/
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     author = {V. N. Dubinin},
     title = {Distortion theorems for circumferentially mean $p$-valent functions},
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     year = {2015},
     volume = {440},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2015_440_a3/}
}
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Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

By symmetrization approach some distortion theorems for circumferentially mean $p$-valent functions are proved. We consider functions with a zero of order $p$ at the origin, functions without zeros and functions with Montel's normalization. All equality cases in the obtained estimates are established.

[1] M. Biernacki, “Sur les fonctions en moyenne multivalentes”, Bull. Sci. Math., 70 (1946), 51–76 | MR | Zbl

[2] W. K. Hayman, Multivalent functions, Secoud ed., Cambridge Univ. Press, Cambridge, 1994 | MR | Zbl

[3] Dzh. Dzhenkins, Odnolistnye funktsii i konformnye otobrazheniya, M., 1962

[4] H. Abe, “On meromorphic and circumferentially mean univalent functions”, J. Math. Soc. Japan, 16:4 (1964), 342–351 | DOI | MR | Zbl

[5] V. N. Dubinin, “Novaya versiya krugovoi simmetrizatsii s prilozheniyami k $p$-listnym funktsiyam”, Mat. sb., 203:7 (2012), 79–94 | DOI | MR | Zbl

[6] V. N. Dubinin, “Simmetrizatsiya kondensatorov i neravenstva dlya mnogolistnykh v kruge funktsii”, Mat. zametki, 94:6 (2013), 846–856 | DOI | MR | Zbl

[7] V. N. Dubinin, “Neravenstva dlya modulei funktsii, $p$-listnykh v srednem po okruzhnosti”, Zap. nauchn. semin. POMI, 429, 2014, 44–54

[8] V. N. Dubinin, “Krugovaya simmetrizatsiya kondensatorov na rimanovykh poverkhnostyakh”, Mat. sb., 206:1 (2015), 69–96 | DOI | MR | Zbl

[9] A. Vasil'ev, Moduli of families of curves for conformal and quasiconformal mappings, Lecture Notes in Math., 1788, Springer, 2002 | DOI | MR | Zbl

[10] V. N. Dubinin, Emkosti kondensatorov i simmetrizatsiya v geometricheskoi teorii funktsii kompleksnogo peremennogo, Dalnauka, Vladivostok, 2009