Abstract
Let 
(α) denote the class of locally univalent normalized analytic functions f in the unit disk |z| < 1 satisfying the condition
and for some 0 < α ≤ 1. We firstly prove sharp coefficient bounds for the moduli of the Taylor coefficients a
n
of f ∈ 
(α). Secondly, we determine the sharp bound for the Fekete-Szegö functional for functions in 
(α) with complex parameter λ. Thirdly, we present a convolution characterization for functions f belonging to 
(α) and as a consequence we obtain a number of sufficient coefficient conditions for f to belong to 
(α). Finally, we discuss the close-to-convexity and starlikeness of partial sums of f ∈ 
(α). In particular, each partial sum s
n
(z) of f ∈ 
(1) is starlike in the disk |z| ≤ 1/2 for n ≥ 11. Moreover, for f ∈ 
(1), we also have Re(s′
n
(z)) > 0 in |z| ≤ 1/2 for n ≥ 11.
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Original Russian Text Copyright © 2013 Obradović M., Ponnusamy S., and Wirths K.-J.
The first author was supported by the MNZZS (Grant ON174017, Serbia).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 4, pp. 852–870, July–August, 2013.
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Obradović, M., Ponnusamy, S. & Wirths, K.J. Coefficient characterizations and sections for some univalent functions. Sib Math J 54, 679–696 (2013). https://doi.org/10.1134/S0037446613040095
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DOI: https://doi.org/10.1134/S0037446613040095