On logarithmic averages of sequences and its applications

Umit Totur, Muhammet A. Okur


In this paper, we investigate summability methods of logarithmic averages of the numerical sequences and its applications such as Tauberian type theorems.


Logarithmic average; logarithmic method; slowly decreasing sequence; Tauberian theorem; Tauberian condition.

Full Text:



method. Analele ?tiin?ifice ale Universit??ii Al.I.Cuza din Ia?i (S.N.)

Matematic?, 61(1):123128.

anak, ?. & Totur, . (2015). A theorem for the (J,p) summability

method. Acta Mathematica Hungarica, 145(1):220228.

Et, M., olak, R. & Altin, Y. (2014a). Strongly almost summable

sequences of order ?. Kuwait Journal of Science, 41(2):3547.

Et, M., Tripathy, B.C. & Dutta, A.J. (2014b). On pointwise statistical

convergence of order ? of sequences of fuzzy mappings. Kuwait

Journal of Science, 41(3):1730.

Hardy, G.H. (1949). Divergent series, Clarendon Press, Oxford.

Kwee, B. (1966). A Tauberian theorem for the logarithmic method of summation. Mathematical Proceedings of the Cambridge Philosophical

Society, 63:401405.

Mricz, F. (2013). Necessary and sufficient Tauberian conditions

for the logarithmic summability of functions and sequences. Studia

Mathematica, 219(2):109121.

Mricz, F. (2006). On the harmonic averages of numerical sequences.

Archiv der Mathematik, 86(4):375384.

Mricz, F. (2004). Theorems relating to statistical harmonic summability

and ordinary convergence of slowly decreasing or oscillating sequences.

Analysis, 24(1-4):127146.

Totur, . & anak, ?. (2012). Some general Tauberian conditions for

the weighted mean summability method. Computers & Mathematics

with Applications, 63:9991006.

Totur, . & Okur, M.A. (2015). Some Tauberian remainder theorems

for Hlder summability. Mathematical Modelling and Analysis,


Ishiguro, K. (1963). Tauberian theorems concerning the summability

method of logarithmic type. Proceedings of the Japan Academy,



  • There are currently no refbacks.