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On Mercer's theorem for (C,2)-means
Authors:Prof P Szüsz
Institution:(1) State University of New York, 11790 Stony Brook, NY, USA
Abstract:A direct proof is given for the following theorem, contained as a special case in a more general result ofPolniakowski:Theorem. Denote sgr n the Cesaro-means of order 2 of the sequenceS 1, S2, ... ,agr any real number satisfying 0<agr<=1. Then 
$$\mathop { \lim }\limits_{n \to \infty } (\alpha S_n  + ((1 - \alpha )\sigma _n ) = S$$
implies 
$$\mathop { \lim }\limits_{n \to \infty } S_n  = S$$
To Prof. Th. Schneider on the occasion of his 65th birthday
Keywords:
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