Bulletin of the Belgian Mathematical Society - Simon Stevin

Coefficient estimates for close-to-convex functions with argument $\beta$

Limei Wang

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Abstract

This paper deals with coefficient estimates for close-to-convex functions with argument $\beta$ ($-\pi/2<\beta<\pi/2$). By using Herglotz representation formula, sharp bounds of coefficients are obtained. In particular, we solve the problem posed by A. W. Goodman and E. B. Saff in [2]$. Finally some complicate computations yield the explicit estimate of the third coefficient.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 18, Number 2 (2011), 231-237.

Dates
First available in Project Euclid: 7 June 2011

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1307452073

Digital Object Identifier
doi:10.36045/bbms/1307452073

Mathematical Reviews number (MathSciNet)
MR2847759

Zentralblatt MATH identifier
1218.30058

Subjects
Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

Keywords
close-to-convex functions with argument $\beta$ coefficient estimate

Citation

Wang, Limei. Coefficient estimates for close-to-convex functions with argument $\beta$. Bull. Belg. Math. Soc. Simon Stevin 18 (2011), no. 2, 231--237. doi:10.36045/bbms/1307452073. https://projecteuclid.org/euclid.bbms/1307452073


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