Abstract. A very general joint result of the author and A. Meir, which gives estimates for pointwise approximation of the function in question by the partial sums of a general orthogonal series, is extended here such that the partial sums are replaced by Cesaro means of negative order; and the external strong summation methods can be taken from the same large family of Hausdorff and $[J,f]$-transformation as in the original theorem.

AMS Subject Classification (1991): 41A25, 41A30, 42C15

Keyword(s): partial sum, pointwise approximation

Received August 6, 1991. (Registered under 5537/2009.)