부산대학교 도서관

Let V3(z, f) and σ(1) 3 (z, f) be the cubic polynomials representing, respectively, the 3rd de la Vall'ee Poussin mean and the 3rd Cesaro mean of order 1 of a power series f(z). If K denotes the usual class of convex univalent functions in the open unit disk centered at the origin, we show that, in general, V3(z, f) ⊀ σ(1) 3 (z, f), for all f ∈ K. Making use of polylogarithms, we identify a transformation, Λ: K → K, such that V3(z, Λ(f)) ≺ σ(1) 3 (z, Λ(f)) for all f ∈ K. Here '≺' stands for subordination between two analytic functions. [ABSTRACT FROM AUTHOR]