Turkish Journal of Mathematics
Abstract
The concepts of strong convergence, statistical convergence, and uniform integrability are of some interest in convergence theories. Recently Ünver and Orhan [19] have introduced the concepts of $P$-strong and $P$-statistical convergences with the help of power series methods and established a relationship between them. In the present paper, we introduce the notion of $P$-strong convergence with respect to an Orlicz function and prove that all these three concepts are boundedly equivalent provided that Orlicz function satisfies $\triangle _{2}-$condition. We also get an improvement of this result by using the concept of uniform integrability.
DOI
10.55730/1300-0098.3126
Keywords
Power series method, strong convergence, statistical convergence, Orlicz function
First Page
832
Last Page
838
Recommended Citation
BAYRAM, NİLAY ŞAHİN
(2022)
"$P$-strong convergence with respect to an Orlicz function,"
Turkish Journal of Mathematics: Vol. 46:
No.
3, Article 11.
https://doi.org/10.55730/1300-0098.3126
Available at:
https://journals.tubitak.gov.tr/math/vol46/iss3/11
