MMN-4949
Estimates on Schippers' higher-order Schwarzian derivatives of a subclass of univalent analytic functions
Zhenyong Hu; Hari Mohan Srivastava; Ying Zhang;Abstract
In the theory of univalent analytic functions, the properties and characteristics of convex functions and starlike functions are widely studied, such as the estimates on Schippers' higher-order Schwarzian derivatives at zero. In this paper, we consider the bounds for Schippers' higher-order Schwarzian derivatives of $f(z)$ at $z=0$ when the function $f$ belongs to the class of a kind of combination of convex functions and starlike functions, which consists of analytic functions $f$ in the open unit disk $\mathbb{D}$ with the normalized conditions given by
$$f(0)=f'(0)-1=0$$
and satisfying the following inequality:
$$\Re \Bigg(\frac{1}{2}\frac{zf'(z)}{f(z)}
+\frac{1}{2}\left(1+\frac{zf''(z)}{f'(z)}\right)\Bigg)>0
\qquad (z\in\mathbb{D}).$$
Vol. 26 (2025), No. 2, pp. 867-875