Univalent polynomials and fractional order differences of their coefficients (Q1014683)

Let \(f(z)=z+\sum_{k=2}^{\infty}a_kz^k\) be analytic in the unit disk \(\mathbb D\). The author finds sufficient conditions on \(\{a_k\}\), \(k\geq2\), such that \(f\) is close-to-convex in \(\mathbb D\). Two theorems refer to polynomials \(f\) while four other theorems of the article treat infinite series. The proofs are based on straightforward estimates of corresponding sums.