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Abstract: In this paper we prove a Tauberian-like theorem to retrieve the slow oscillation of a real-valued function from its summability of the generator sequence and one-sidedly boundedness of the general control modulo of integer order with respect to a function satisfying an appropriate condition. [Copyright &y& Elsevier]

Abstract: In this paper, we prove Tauberian theorems of slowly oscillating type for the summability method by using a result due to Mikhalin [G.A. Mikhalin, Theorem of Tauberian type for (J, pn) summation methods, Ukrain. Mat. Zh. 29 (1977), 763–770. English translation: Ukrain. Math. J. 29 (1977) 564–569]. [Copyright &y& Elsevier]

Abstract: The object of this work is to retrieve the convergence of a series from its discrete summability under certain conditions. We obtain as a corollary a Tauberian theorem for the discrete logarithmic summability method. [Copyright &y& Elsevier]

Abstract: Let 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 of a sequence , under which, convergence follows from the Abel summability. These are generalizations of some of the well-known classical Tauberian conditions. [Copyright &y& Elsevier]

Abstract: In this paper, we obtain some new Tauberian theorems for the weighted mean summability method via a weighted general control modulo analogous to the one defined by Dik [M. Dik, Tauberian theorems for sequences with moderately oscillatory control moduli, Math. Morav. 5 (2001) 57–94]. [Copyright &y& Elsevier]

Abstract: Let be a real valued function which is continuous on . In this paper we prove a Tauberian-like theorem to retrieve slow oscillation of out of its summability of the generator function and some additional conditions. As a corollary we recover convergence of . [Copyright &y& Elsevier]

Abstract: In this paper, we give alternative proofs of some classical type Tauberian theorems for the Cesàro summability of improper integrals. [Copyright &y& Elsevier]

Abstract: In this paper, we establish some Tauberian theorems for the Abel summability method in terms of regularly generated sequences which generalizes some results obtained in Çanak and Totur [İ. Çanak, Ü. Totur, A note on Tauberian theorems for regularly generated sequences, Tamkang J. Math. 39 (2) (2008) 187–191]. [Copyright &y& Elsevier]

Abstract: In this paper we introduce some Tauberian conditions for the (A)(C, α) summability method. These results extend and generalize some of the classical Tauberian theorems for the Abel summability method. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce the concept of the weighted generator sequence and prove that certain conditions in terms of weighted generator sequences are Tauberian conditions for the weighted mean summability method. [Copyright &y& Elsevier]

Abstract: In this paper we generalize some classical type Tauberian theorems given for Cesàro summability of integrals. [Copyright &y& Elsevier]

Abstract: In this paper, we introduce some conditions to recover subsequential convergence of an summable sequence which is one-sidedly bounded by another sequence. [Copyright &y& Elsevier]

Abstract: In this paper we give a proof of the generalized Littlewood Tauberian theorem for Cesàro summability of improper integrals. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we retrieve the backward Cesàro convergence of a real sequence from the Cesàro summability of the general control modulo of the oscillatory behavior of integer order of under certain conditions. [Copyright &y& Elsevier]

Abstract: In this paper we give some sufficient conditions in terms of regularly generated sequences for a sequence to be subsequentially convergent. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, we show under which conditions a generator sequence is convergent. We also give a Tauberian theorem for Cesàro summability as a special case. [ABSTRACT FROM AUTHOR]

Abstract: In this work we prove that one-sided slow oscillation of a sequence and that of its generator sequence are Tauberian conditions for the Abel summability method, using a corollary to Karamata’s Main Theorem [J. Karamata, Über die Hardy–Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes, Math. Z. 32 (1930) 319–320]. It is also shown that such conditions are Tauberian conditions for generalized Abelian summability methods. [ABSTRACT FROM AUTHOR]

Abstract: In this paper we prove a Tauberian theorem for summability method, which extends the well-known classical Tauberian theorem due to Tauber [A. Tauber, Ein satz der Theorie der unendlichen Reihen, Monatsh. f. Math. 8 (1897) 273–277]. [Copyright &y& Elsevier]

Abstract: In this paper we give some Tauberian conditions in order to obtain summability from summability. [Copyright &y& Elsevier]

Abstract: In this paper, a new concept of Δ-quasi-slowly oscillating continuity is introduced. Furthermore, it is shown that this kind of continuity implies ordinary continuity. A new type of compactness is also defined and some new results related to compactness are proved. [Copyright &y& Elsevier]

Abstract: In this paper we retrieve slow oscillation of a real sequence from Cesàro summability of its generator sequence under some one-sided condition. [Copyright &y& Elsevier]

Abstract: We investigate the conditions needed for a Borel summable sequence to be convergent. The results of this paper extend and improve the well-known result of Hardy and Littlewood (1913) . [Copyright &y& Elsevier]

Abstract: In this paper, some one-sided Tauberian conditions for summability method have been obtained. [Copyright &y& Elsevier]

Abstract: Let be a sequence, regularly generated by another sequence where either or is slowly oscillating. We investigate conditions under which the sequence converges or converges subsequentially. [Copyright &y& Elsevier]

Abstract: Let be a sequence of real numbers such that and , where and . We prove that and if the following conditions hold: where denotes the integer part of . [Copyright &y& Elsevier]

Abstract: In this work we give an alternative proof of the generalized Littlewood Tauberian theorem for the Abel summability method using a corollary to Karamata’s Main Theorem [J. Karamata, Über die Hardy–Littlewoodschen Umkehrungen des Abelschen Stetigkeitssatzes, Math. Z. 32 (1930) 319–320]. [Copyright &y& Elsevier]

Abstract: In this work, we introduce some classical and neoclassical Tauberian-like conditions to retrieve subsequential convergence of a real sequence and some other sequences related to it out of the boundedness of the sequence . Consequently we obtain significant information about subsequential behavior of the sequence. [Copyright &y& Elsevier]