NECESSARY AND SUFFICIENT TAUBERIAN CONDITIONS UNDER WHICH STATISTICALLY LOGARITHMIC CONVERGENCE FOLLOWS FROM STATISTICALLY LOGARITHMIC SUMMABILITY
Articles > Article · 2023
Authors: Nergiz Çinar, İbrahim ÇANAK
Journal of Classical Analysis, International, Scopus, 2023, vol 21, pp 29-34
Summary
Let (sn) be a sequence of complex numbers. The sequence (τn) of n-th logarithmic means of (sn) is defined by (formula presented). It is well known that if a bounded sequence (sn) is statistically logarithmic convergent to s, then it is statistically logarithmic summable to the same number. However, the converse of this implication is not true in general. In this paper, we obtain conditions, so called Tauberian conditions, under which the converse implication holds.