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Fekete–Szegö Problem for a Certain Subclass of Close-to-convex Functions

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Abstract

Given a starlike function \(g\in \mathcal S^*,\) an analytic standardly normalized function \(f\) in the unit disk \(\mathbb {D}\) is called close-to-convex with respect to \(g\) if there exists \(\delta \in (-\pi /2,\pi /2)\) such that

$$\begin{aligned} {{\mathrm{Re}}}\left\{ \mathrm{e}^{i\delta }\frac{zf'(z)}{g(z)}\right\} >0,\quad z\in \mathbb {D}. \end{aligned}$$

For the class \(\mathcal C(h)\) of all close-to-convex functions with respect to \(h(z):=z/(1-z),\ z\in \mathbb {D},\) a Fekete–Szegö problem is examined.

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Authors and Affiliations

  1. Chair of Complex Analysis, University of Warmia and Mazury, ul. Słoneczna 54, 10-710, Olsztyn, Poland

    Bogumiła Kowalczyk & Adam Lecko

Authors
  1. Bogumiła Kowalczyk
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  2. Adam Lecko
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Correspondence to Adam Lecko.

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Communicated by V. Ravichandran.

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Kowalczyk, B., Lecko, A. Fekete–Szegö Problem for a Certain Subclass of Close-to-convex Functions. Bull. Malays. Math. Sci. Soc. 38, 1393–1410 (2015). https://doi.org/10.1007/s40840-014-0091-z

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  • DOI: https://doi.org/10.1007/s40840-014-0091-z

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