Extended Tauberian Theorem for the weighted mean Method of Summability
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We prove a new Tauberian-like theorem. For a real sequence u = (u n ), on the basis of the weighted mean summability of its generator sequence (V (0) n,p (∆u)) and some other conditions, this theorem establishes the property of slow oscillation of the indicated sequence.
KeywordsOscillatory Behavior Real Sequence Sequence Versus Summability Method Integer Order
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