Abstract
In the present paper, we introduce the notion of \(\mathfrak{B}\) -strong convergence with respect to an Orlicz function and prove that \(\mathfrak{B}\) -strong convergence, \(\mathfrak{B}\) -statistical convergence, and \(\mathfrak{B}\) -strong convergence with respect to an Orlicz function 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.
