Tauberian conditions with controlled oscillatory behavior |
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| Authors: | ?brahim Çanak Bilender P Allahverdiev |
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| Institution: | a Department of Mathematics, EGE University, ?zmi?r 35100, Turkeyb Department of Mathematics, Adnan Menderes University, Aydin 09010, Turkeyc Department of Mathematics, Suleyman Demi?rel University, Isparta 32260, Turkey |
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| Abstract: | Let (un) be a sequence of real numbers. In this paper, we give new Tauberian conditions imposed on the general control modulo of the oscillatory behavior of integer order m≥1 of a sequence (un), under which, convergence follows from the Abel summability. These are generalizations of some of the well-known classical Tauberian conditions. |
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| Keywords: | General control modulo Tauberian conditions Slow oscillation One-sided slow oscillation Slow decreasing |
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