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Schmidt’s classical Tauberian theorem says that if a sequence (sk : 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 complexvalued 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.

Statistical extensions of some classical Tauberian theorems in nondiscrete setting