Tauberian conditions for a general limitable method

Let (un) be a sequence of real numbers, L an additive limitable method with some property, and and different spaces of sequences related to each other. We prove that if the classical control modulo of the oscillatory behavior of (un) in is a Tauberian condition for L, then the general control modulo of the oscillatory behavior of integer order m of (un) in or is also a Tauberian condition for L

A Tauberian theorem for Cesàro summability of integrals

AbstractIn this paper we give a proof of the generalized Littlewood Tauberian theorem for Cesàro summability of improper integrals

Tauberian theorems for sequences whose oscillations are controlled

Bu tezde, Karamata’nın temel teoremi ve sonucunun yardımıyla, klasik Tauber teorisinde elde edilmi¸s olan sonuc .ların yeniden ispatlanması ve genelle¸sti rilmelerinin verilmesi amac .lanmı¸stır. 1. B¨olu¨mde teze giri¸s yapılmı¸stır. 2. B¨olu¨mde, tez boyunca kullanılacak olan tanımlar ve g¨osterimler ve rilmi¸s, klasik Tauber teorisinin geli¸siminden bahsedilmi¸stir. 3. B¨olu¨mde, kontrol modu¨lo kavramı ile klasik Tauber teoremleri genelle¸sti rilmi¸stir. 4. B¨olu¨mde, alt dizisel Tauber teorisi tanıtılıp, bununla ilgili Tauber teo remleri verilmi¸stir.In this work, it is aimed to collect the results in the classical Tauberian theory and to give their generalizations by mean of Karamata’s Hauptsatz and its corollary. In Chapter 1, introduction is done to thesis. In Chapter 2, all the definitions and notations used in the thesis are given and the state of arts for the classical Tauberian theory is examined. In Chapter 3, classical Tauberian theorems are generalized by the concept of control modulo. In Chapter 4, subsequential Tauberian theory is introduced and then Tauberian theorems related to it are given

A Tauberian theorem for the discrete Mφ summability method

AbstractThe object of this work is to retrieve the convergence of a series from its discrete Mφ summability under certain conditions. We obtain as a corollary a Tauberian theorem for the discrete logarithmic summability method

Tauberian theorems for statistically (C,1,1) summable double sequences of fuzzy numbers

In this paper, we prove that a bounded double sequence of fuzzy numbers which is statistically convergent is also statistically (C, 1, 1) summable to the same number. We construct an example that the converse of this statement is not true in general. We obtain that the statistically (C, 1, 1) summable double sequence of fuzzy numbers is convergent and statistically convergent to the same number under the slowly oscillating and statistically slowly oscillating conditions in certain senses, respectively

SOME CONDITIONS UNDER WHICH SUBSEQUENTIAL CONVERGENCE FOLLOWS FROM (A, m) SUMMABILITY

In this paper, we obtain some conditions on a sequence under which subsequential convergence [Math. Morav. 5, 19-56 (2001; Zbl 1047.40005)] of the sequence follows from its (A, m) summability.

A Tauberian Theorem with a Generalized One-Sided Condition

We prove a Tauberian theorem to recover moderate oscillation of a real sequence u=(un) out of Abel limitability of the sequence (Vn(1)(Δu)) and some additional condition on the general control modulo of oscillatory behavior of integer order of u=(un)