The statistical and strong p-Cesaro convergence of sequences. (English) Zbl 0653.40001

Connor, J. S.

Analysis 8, No. 1-2, 47-63 (1988).

Summary: It is shown that if a sequence is strongly p-Cesàro summable or \(w_ p\) convergent for \(0<p<\infty\) then the sequence must be statistically convergent and that a bounded statistically convergent sequence must be \(w_ p\) convergent for any p, \(0<p<\infty\). It is also shown that the statistically convergent sequences do not form a locally convex FK space. A characterization of conservative matrices which map the bounded statistically convergent sequences into convergent sequences is given and applied to Nörlund and Nörlund-type means.

MSC:

40A05	Convergence and divergence of series and sequences
40D25	Inclusion and equivalence theorems in summability theory
40D09	Structure of summability fields
40C05	Matrix methods for summability
40H05	Functional analytic methods in summability

Keywords:

Cesàro convergence; bounded statistically convergent sequence; locally convex FK space; Nörlund-type means