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.