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Displaying similar documents to “Tauberian theorems for Cesàro summable double integrals over ℝ + 2 ”

Statistical extensions of some classical Tauberian theorems in nondiscrete setting

Ferenc Móricz (2007)

Colloquium Mathematicae

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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...

Ordinary convergence follows from statistical summability (C,1) in the case of slowly decreasing or oscillating sequences

Ferenc Móricz (2004)

Colloquium Mathematicae

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Schmidt’s Tauberian theorem says that if a sequence (xk) of real numbers is slowly decreasing and l i m n → ∞ ( 1 / n ) ∑ k = 1 n x k = L , then l i m k → ∞ x k = L . The notion of slow decrease includes Hardy’s two-sided as well as Landau’s one-sided Tauberian conditions as special cases. We show that ordinary summability (C,1) can be replaced by the weaker assumption of statistical summability (C,1) in Schmidt’s theorem. Two recent theorems of Fridy and Khan are also corollaries of our Theorems 1 and 2. In the Appendix, we present a new proof...