Abstract
It is well known that not every summability method implies the strong summability with any positive exponent. We give easygoing additional conditions on the terms of a positive regular Toeplitz-matrix implying the strong summability for any positive exponent. The classical (C, α > 0)- and Abel-summabilities satisfy our conditions plainly. We treat the generalized Abel, the Euler, the Riesz and the generalized de la Vallee Poussin methods, as well.
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