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 unver 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 o2- condition. We also get an improvement of this result by using the concept of uniform integrability.