Geodesic
Inequalities for moduli of the circumferentially mean $p$-valent functions
Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 44-54 Cet article a éte moissonné depuis la source Math-Net.Ru

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Let $f$ be a circumferentially mean $p$-valent function in the disk $|z|<1$ with Montel's normalization: $f(0)=0$, $f(\omega)=\omega$ $(0<\omega<1)$. Under an additional constraint on the covering of the concentric circles by $f$, precise lower and upper bounds of modulus $|f(z)|$ for some $z\in(-1,0)$ are established. The necessity of such constraint for the non-trivial estimates to be true is shown. 
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V. N. Dubinin. Inequalities for moduli of the circumferentially mean $p$-valent functions. Zapiski Nauchnykh Seminarov POMI, Analytical theory of numbers and theory of functions. Part 29, Tome 429 (2014), pp. 44-54. http://geodesic.mathdoc.fr/item/ZNSL_2014_429_a4/

[1] P. Montel, Lecons sur les fonctions univalentes ou multivalentes, Gauthier-Villars, Paris, 1933 | Zbl

[2] J. Krzyz, “On univalent functions with two preassigned values”, Ann. Univ. Mariae Curie-Sklodowska, Sec. A, 15:5 (1961), 57–77 | MR | Zbl

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

[4] V. Singh, “Some extremal problems for a new class of univalent functions”, J. Math. Mech., 7 (1958), 811–821 | MR | Zbl

[5] Z. Lewandowski, “Sur certaines classes de fonctions univalentes dans le cercleunité”, Ann. Univ. Mariae Curie-Sklodowska, Sec. A, 13:6 (1959), 115–126 | MR

[6] J. Krzyz, E. Zlotkiewicz, Koebe sets for univalent functions with two preassigned values, Ann. Acad. Sci. Fenn. Ser. A1. Math., 487, 1971, 12 pp. | MR | Zbl

[7] R. J. Libera, E. J. Zlotkiewicz, “Bounded Montel univalent functions”, Collog. Math., 56 (1988), 169–177 | MR | Zbl

[8] A. Vasil'ev, P. Pronin, “On some extremal problem for bounded univalent functions with Montel's normalization”, Demonstratio Math., 26 (1993), 703–707 | MR | Zbl

[9] A. Vasil'ev, P. Pronin, “The range of a system of functionals for the Montel univalent functions”, Bol. Soc. Mat. Mexicana, 6 (2000), 147–190 | MR

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

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

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

[13] V. N. Dubinin, “K teoreme Dzhenkinsa o pokrytii okruzhnostei golomorfnymi v kruge funktsiyami”, Zap. nauchn. semin. POMI, 418, 2013, 60–73

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

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