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Open AccessArticle

Hankel Determinants for Univalent Functions Related to the Exponential Function

Faculty of Mechanical Engineering, Lublin University of Technology, 20-618 Lublin, Poland
Symmetry 2019, 11(10), 1211; https://doi.org/10.3390/sym11101211
Received: 16 September 2019 / Revised: 24 September 2019 / Accepted: 25 September 2019 / Published: 28 September 2019
Recently, two classes of univalent functions S e * and K e were introduced and studied. A function f is in S e * if it is analytic in the unit disk, f ( 0 ) = f ( 0 ) 1 = 0 and z f ( z ) f ( z ) e z . On the other hand, g K e if and only if z g S e * . Both classes are symmetric, or invariant, under rotations. In this paper, we solve a few problems connected with the coefficients of functions in these classes. We find, among other things, the estimates of Hankel determinants: H 2 , 1 , H 2 , 2 , H 3 , 1 . All these estimates improve the known results. Moreover, almost all new bounds are sharp. The main idea used in the paper is based on expressing the discussed functionals depending on the fixed second coefficient of a function in a given class. View Full-Text
Keywords: Hankel determinant; starlike functions; convex functions; exponential function Hankel determinant; starlike functions; convex functions; exponential function
MDPI and ACS Style

Zaprawa, P. Hankel Determinants for Univalent Functions Related to the Exponential Function. Symmetry 2019, 11, 1211.

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