TAUBERIAN-AND CONVEXITY THEOREMS FOR CERTAIN (N,P,Q)-MEANS

The summability fields of generalized Norlund means (N,palpha,p) alph a is-an-element-of N, are increasing with a and are contained in that of the corresponding power series method (P,p). Particular cases are t he Cesaro- and Euler-means with corresponding power series methods of Abel and Borel. In this paper we generalize a convexity theorem, which is well-known for the Cesaro means and which was recently shown for t he Euler means to a large class of generalized Norlund means.