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• # Artykuł - szczegóły

## Colloquium Mathematicum

2007 | 107 | 1 | 45-56

## Statistical extensions of some classical Tauberian theorems in nondiscrete setting

EN

### Abstrakty

EN
Schmidt's classical Tauberian theorem says that if a sequence $(s_{k}: k = 0,1,...)$ of real numbers is summable (C,1) to a finite limit and slowly decreasing, then it converges to the same limit. In this paper, we prove a nondiscrete version of Schmidt's theorem in the setting of statistical summability (C,1) of real-valued functions that are slowly decreasing on ℝ ₊. We prove another Tauberian theorem in the case of complex-valued functions that are slowly oscillating on ℝ ₊. In the proofs we make use of two nondiscrete analogues of the famous Vijayaraghavan lemma, which seem to be new and may be useful in other contexts.

45-56

wydano
2007

### Twórcy

autor
• Bolyai Institute, University of Szeged, Aradi vértanúk tere 1, 6720 Szeged, Hungary