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http://dx.doi.org/10.5666/KMJ.2021.61.3.513

On Coefficients of a Certain Subclass of Starlike and Bi-starlike Functions  

Mahzoon, Hesam (Department of Mathematics, Islamic Azad University)
Sokol, Janusz (College of Natural Sciences, University of Rzeszow)
Publication Information
Kyungpook Mathematical Journal / v.61, no.3, 2021 , pp. 513-522 More about this Journal
Abstract
In this paper we investigate a subclass 𝓜(α) of the class of starlike functions in the unit disk |z| < 1. 𝓜(α), π/2 ≤ α < π, is the set of all analytic functions f in the unit disk |z| < 1 with the normalization f(0) = f'(0) - 1 = 0 that satisfy the condition $$1+\frac{{\alpha}-{\pi}}{2\;sin\;{\alpha}}k)]1/k. Also a certain subclass of bi-starlike functions is introduced and the bounds for the initial coefficients are obtained.
Keywords
analytic functions; starlike and bi-starlike functions; subordination; Fekete-Szego inequality;
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