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Abstract: Let be a sequence of real numbers and be an additive summability method with some property. We show that if slow decrease of or one-sided boundedness of the classical control modulo of the oscillatory behavior of is a Tauberian condition for a general summability method , then one-sided boundedness by a sequence with certain conditions of the general control modulo of the oscillatory behavior of integer order of is also a Tauberian condition for . [Copyright &y& Elsevier]

Abstract: In this paper, we introduce some new Tauberian-like conditions to retrieve slow oscillation of a real sequence out of summability of its generator sequence. [ABSTRACT FROM AUTHOR]

Abstract: Let be a sequence of real numbers. We obtain some Tauberian-like conditions in terms of the general control modulo of integer order to retrieve subsequential convergence of from the boundedness of . [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]

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