One-sided Tauberian conditions for a general summability method

@article{Totur2011OnesidedTC,
  title={One-sided Tauberian conditions for a general summability method},
  author={{\"U}mit Totur and Mehmet Dik},
  journal={Mathematical and Computer Modelling},
  year={2011},
  volume={54},
  pages={2639-2644}
}
Let (un) be a sequence of real numbers and L be an additive summability method with some property. We show that if slow decrease of (un) or one-sided boundedness of the classical control modulo of the oscillatory behavior of (un) is a Tauberian condition for a general summability method L, then one-sided boundedness by a sequence with certain conditions of the general control modulo of the oscillatory behavior of integer order m of (un) is also a Tauberian condition for L. © 2011 Elsevier Ltd… CONTINUE READING
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