Turkish Journal of Mathematics
DOI
10.55730/1300-0098.3126
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.
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
