Tauberian theorems for double sequences that are statistically summable \((C,1,1)\). (English) Zbl 1028.40002

The author considers real and complex double sequences \((x_{jk})\) and compares statistical convergence and statistical convergence of their Cesàro means \((C,1,1) .\) For a bounded sequence \((x_{jk})\) statistical convergence to a limit \(s\) implies statistical convergence of its Cesàro means to the same limit. The two main results of the present paper give necessary and sufficient conditions, respectively two-sided Tauberian conditions for the reverse implication. The Tauberian conditions given are statistical versions of certain slow oscillation conditions. The results extend corresponding theorems by the author from ordinary sequences to double sequences; see F. Móricz [J. Math. Anal. Appl. 275, 277-287 (2002; Zbl 1021.40002)].


40E05 Tauberian theorems


Zbl 1021.40002
Full Text: DOI


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