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

Abstract

Let C0(h) be a subclass of analytic and close-to-convex functions defined in the open unit disk by the formula ()(1−z2)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.