Notes on the norm of pre-Schwarzian derivatives of certain analytic functions

Authors

DOI:

https://doi.org/10.24193/subbmath.2020.3.04

Keywords:

Analytic, univalent, locally univalent, subordination, pre-Schwarzian norm.

Abstract

In this paper, we obtain sharp bounds for the norm of pre-Schwarzian derivatives of certain analytic functions. Initially this problem was handled by H. Rahmatan, Sh. Najafzadeh and A. Ebadian [Stud. Univ. Babe¸s-Bolyai Math. 61(2016), no. 2, 155-162]. We pointed out that their proofs are incorrect and present correct proofs.

Mathematics Subject Classification (2010): 30C45.

References

Becker, J., Pommerenke, Ch., Schlichtheitskriterien und Jordangebiete, J. Reine Angew. Math., 354(1984), 74-94.

Choi, J.H., Kim, Y.C., Ponnusamy, S., Sugawa, T., Norm estimates for the Alexander transforms of convex functions of order alpha, J. Math. Anal. Appl., 303(2005), no. 2, 661-668.

Duren, P.L., Univalent Functions, Springer-Verlag, New York, 1983.

Kim, Y.C., Sugawa, T., Growth and coefficient estimates for uniformly locally univalent functions on the unit disk, Rocky Mountain J. Math., 32(2002), no. 1, 179-200.

Kargar, R., Ebadian, A., Soko´l-, J., On subordination of some analytic functions, Sib. Math. J., 57(2016), no. 4, 599-605.

Kargar, R., Ebadian, A., Soko´l-, J., Some properties of analytic functions related with bounded positive real part, Int. J. Nonlinear Anal. Appl., 8(2017), no. 1, 235-244.

Kuroki, K., Owa, S., Notes on new class for certain analytic functions, RIMS Kokyuroku Kyoto Univ., 1772(2011), 21-25.

Nehari, Z., Conformal Mapping, McGraw-Hill, New York, 1952.

Ponnusamy, S., Sahoo, S.K., Sugawa, T., Radius problems associated with preSchwarzian and Schwarzian derivatives, Analysis, 34(2014), no. 2, 163-171.

Rahmatan, H., Najafzadeh, Sh., Ebadian, A., The norm of pre-Schwarzian derivatives of certain analytic functions with bounded positive real part, Stud. Univ. Babe¸s-Bolyai Math., 61(2016), no. 2, 155-162.

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Published

2020-09-15

How to Cite

KARGAR, R. (2020). Notes on the norm of pre-Schwarzian derivatives of certain analytic functions. Studia Universitatis Babeș-Bolyai Mathematica, 65(3), 357–363. https://doi.org/10.24193/subbmath.2020.3.04

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