Ukr. Mat. Zh. - 2018. - 70, № 6. - pp. 848-858
We extend some results known from the literature for ordinary (single) sequences to multiple sequences of real numbers. Further, we introduce a concept of double lacunary strong $(A, ϕ)$-convergence with respect to a modulus function. In addition, we also study some relationships between double lacunary strong $(A, ϕ)$-convergence with respect to a modulus and double lacunary statistical convergence.
Ukr. Mat. Zh. - 2017. - 69, № 3. - pp. 324-331
Following the line of the recent work by Sava¸s et al., we apply the notion of ideals to $A$-statistical cluster points. We get necessary conditions for the two matrices to be equivalent in a sense of $A^I$ -statistical convergence. In addition, we use Kolk’s idea to define and study $B^I$ -statistical convergence.
Ukr. Mat. Zh. - 2016. - 68, № 12. - pp. 1598-1606
We consider the notion of generalized density, namely, natural density of weight g recently introduced in [Balcerzak M., Das P., Filipczak M., Swaczyna J. Generalized kinds of density and the associated ideals // Acta Math. Hung. – 2015. –147, № 1. – P. 97 – 115] and primarily study some sufficient and almost converse necessary conditions for the generalized statistically convergent sequence under which the subsequence is also generalized statistically convergent. Some results are also obtained in more general form using the notion of ideals. The entire investigation is performed in the setting of general metric spaces extending the recent results of Kucukaslan M., Deger U., Dovgoshey O. On statistical convergence of metric valued sequences, see Ukr. Math. J. – 2014. – 66, № 5. – P. 712 – 720.
Ukr. Mat. Zh. - 2016. - 68, № 9. - pp. 1251-1258
We introduce а new notion, namely, $I_\lambda$-double statistical convergence of order \alpha in topological groups. Consequently, we investigate some inclusion relations between $I$ -double statistical and $I_\lambda$ -double statistical convergence of order $\alpha$ in topological groups. We also study many other related concepts.