Tauberian theorems for statistically convergent double sequences
In [F. Moricz, Tauberian theorems for Cesro summable double sequences, Studia Math. 110 (1994) 8396], Moricz has proved some Tauberian theorems for Cesro summable double sequences and deduced the Tauberian theorems of Landau [E. Landau, ber die Bedeutung einiger neuerer Grenzwertstze der Herren Hardy and Axer, Prac. Mat.-Fiz. 21 (1910) 97177] and Hardy [G.H. Hardy, Divergent Series, Univ. Press, Oxford 1956] type. In [J.A. Fridy, M.K. Khan, Statistical extension of some classical Tauberian theorems, Proc. Amer. Math. Soc. 128 (2000) 23472355], Fridy and Khan have given statistical extensions of some classical Tauberian theorems. The concept of statistical convergence for double sequences has recently been introduced by Mursaleen and Edely [M. Mursaleen, Osama H. H. Edely, Statistical convergence of double sequences, J. Math. Anal. Appl. 288 (2003) 223231] and by Moricz [F. Moricz, Statistical convergence of multiple sequences, Arch. Math. 81 (2003) 8289] independently. In this paper we give some Tauberian theorems for statistically convergent double sequences. We have also provided some examples including an example to Problem 1 of Moricz [F. Moricz, Tauberian theorems for Cesro summable double sequences, Studia Math. 110 (1994) 8396].
statistical convergence double sequence convergence in pringsheims sense summability c11 c10 and c01 tauberian condition