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Estimates of Coefficient Functionals for Functions Convex in the Imaginary-Axis Direction

Faculty of Mechanical Engineering, Lublin University of Technology, ul. Nadbystrzycka 36, 20-618 Lublin, Poland
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Symmetry 2020, 12(10), 1736; https://doi.org/10.3390/sym12101736
Received: 11 September 2020 / Revised: 13 October 2020 / Accepted: 19 October 2020 / Published: 20 October 2020
(This article belongs to the Special Issue Symmetry in Geometric Functions and Mathematical Analysis)
Let C0(h) be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula Re{(1z2)f(z)}>0. In this paper, some coefficient problems for C0(h) are considered. Some properties and bounds of several coefficient functionals for functions belonging to this class are provided. The main aim of this paper is to find estimates of the difference and of sum of successive coefficients, bounds of the sum of the first n coefficients and bounds of the n-th coefficient. The obtained results are used to determine coefficient estimates for both functions convex in the imaginary-axis direction with real coefficients and typically real functions. Moreover, the sum of the first initial coefficients for functions with a positive real part and with a fixed second coefficient is estimated. View Full-Text
Keywords: close-to-convex functions; convexity in imaginary-axis direction; coefficient problems; typically real functions; successive coefficients close-to-convex functions; convexity in imaginary-axis direction; coefficient problems; typically real functions; successive coefficients
MDPI and ACS Style

Zaprawa, P.; Tra̧bka-Wiȩcław, K. Estimates of Coefficient Functionals for Functions Convex in the Imaginary-Axis Direction. Symmetry 2020, 12, 1736.

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