On a conjecture of S.P. Robinson ✩

In his thesis, S.P. Robinson made a conjecture concerning the polynomials P β n (z) = 1+ n k=1 k−1 j=0 n− j β + n+ j zk, n∈ N, β 1, namely that zP β n is prestarlike of order (3−β)/2. These polynomials are closely related to the de la Vallée Poussin means (the case β = 1). We prove this conjecture in a more general form and show that these functions constitute a sort of two-dimensional subordination chain. These results are then compared with similar ones for Cesáro means of various orders.  2005 Elsevier Inc. All rights reserved