Geometric properties of Cesaro averaging operators

摘要

In this paper, using positivity of trigonometric cosine and sine sums whosecoefficients are generalization of Vietoris numbers, we find the conditions onthe coefficient $\{a_k\}$ to characterize the geometric properties of thecorresponding analytic function $f(z)=z+\displaystyle\sum_{k=2}^{\infty}a_kz^k$ in the unit disc $\mathbb{D}$. As an application we also find geometricproperties of a generalized Ces\`aro type polynomials.