On strong matrix summability with respect to a modulus and statistical convergence. (English) Zbl 0693.40007

Connor, Jeff

Can. Math. Bull. 32, No. 2, 194-198 (1989).

The definition of strong Cesaro summability with respect to a modulus is extended to a definition of strong A-summability with respect to a modulus when A is a nonnegative regular matrix summability method. It is shown that if a sequence is strongly A-summable with respect to an arbitrary modulus then it is A-statistically convergent and that A- statistical convergence and strong A-summability with respect to a modulus are equivalent on the bounded sequences.

Reviewer: B.P.Mishra

MSC:

40D25	Inclusion and equivalence theorems in summability theory
40A05	Convergence and divergence of series and sequences

Keywords:

strong Cesaro summability; strong A-summability