P -strong convergence with respect to an Orlicz function

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 △2−condition. We also get an improvement of this result by using the concept of uniform integrability.