Tauberian theorems for statistical convergence

Erdal Gul, Mehmet Albayrak

Abstract


The Tauberian theorems for statistical limitable method are proved by both Fridy and Khan \cite{3} and M\'oricz \cite{28}. Here we generalize these theorems to (C; i) statistical limitable method.

Keywords


Statistical convergence, Tauberian theorems, Slowly oscillating.

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References


H. D. Armitage and J. I. Maddox, Discrete Abel mean}, Analysis, 10(1990), 177--186.

A. J. Fridy and M. K. Khan, Statistical extension of some classical Tauberian theorems, Proc. Amer. Math. Soc. 18(2000), 2347--2355.

E. Gul and M. Albayrak, On Abel convergent series of functions, Journal of Advances in Mathematics. 11(9)(2016), 5639--5644.

H. G. Hardy, Theorems relating to the summability and convergence of slowly oscillating series, Proc. London Math Soc., 8(2)(1910), 310--320.

H. G. Hardy and J. E. Littlewood, Tauberian theorems concerning power series and Dirichlet's series whose coecients are positive, Proc. London Math.Soc., 13(2)(1914), 174--191.

E. Landau, Uber die Bedeutung einiger neuen Grenzwertsatze der Herren Hardy und Axer, Prace Mat.-Fiz. 21(1910), 97--177.

B. Kwee, A Tauberian theorem for the logaritmic method of summation, Math. Proc. Comb. Phil. Soc., 63(1967), 97--177.

F. Moricz, Tauberian conditions, under which statistical convergence follows from statistical summability (C,1), J. Math. Anal. Appl., 275(2002), 277--287.

F. Moricz and Z. Nemeth, Statistical extension of classical Tauberian theorems in the case of logarithmic summability, Analysis Math., 40(2014).

F. Moricz, Ordinary convergence follows from statistical summability (C,1) in the case of slowly decreasing or oscillating sequences, Analysis, 24(2004), 127--145.

R. Schmidt, Uber divergente Folgen und lineare Mittelbildungen, Math. Z., 22(1925), 89--152.




DOI: http://dx.doi.org/10.5556/j.tkjm.48.2017.2406

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