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

中文翻译：

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虚轴方向凸函数的系数泛函估计

令 C0(h) 是由公式 Re{(1−z2)f'(z)}>0 在开单位圆盘中定义的解析函数和接近凸函数的子类。在本文中，考虑了 C0(h) 的一些系数问题。提供了属于此类的函数的几个系数泛函的一些属性和界限。本文的主要目的是找到连续系数的差值和总和的估计值、前 n 个系数的总和的界限以及第 n 个系数的界限。获得的结果用于确定在虚轴方向上具有实系数和通常为实函数的两个凸函数的系数估计。此外，估计具有正实部和固定第二系数的函数的第一初始系数之和。