Abstract. We verify that in a divergence theorem proved by L.~Csernyák and the author the classical monotone decreasing assumption on the ``blocksequence'' can be weakened to locally almost monotone condition. Furthermore by means of the new result we improve a theorem pertaining to the divergence of the generalized de la Vallée-Poussin means.

DOI: 10.14232/actasm-013-287-z

AMS Subject Classification (1991): 42A20, 42A16

Keyword(s): orthogonal series, coefficient conditions, locally almost monotonicity

Received June 14, 2013, and in revised form July 24, 2013. (Registered under 37/2013.)