On $A$-statistical convergence and $A$-statistical Cauchy via ideal

Keywords: $I$-convergence, $A^{I}$-statistical convergence, $A^{I^{\ast }}$-statistical convergence, $A^{I}$-statistical Cauchy convergence, $A^{I^{\ast }}$-statistical Cauchy convergence
Published online: 2022-12-30

Abstract


In [Analysis 1985, 5 (4), 301-313], J.A. Fridy proved an equivalence relation between statistical convergence and statistical Cauchy sequence. In this paper, we define $A^{I^{\ast }}$-statistical convergence and find under certain conditions, that it is equivalent to $A^{I}$-statistical convergence defined in [Appl. Math. Lett. 2012, 25 (4), 733-738]. Moreover, we define $A^{I}$-  and $A^{I^{\ast }}$-statistical Cauchy sequences and find some equivalent relation with $A^{I}$-  and $A^{I^{\ast }}$-statistical convergence.

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How to Cite
(1)
Edely O., Mursaleen M. On $A$-Statistical Convergence and $A$-Statistical Cauchy via Ideal. Carpathian Math. Publ. 2022, 14 (2), 442-452.