New summability methods via $\widetilde{\phi}$ functions

Abstract

In 1971, the definition of Orlicz $\widetilde{\phi}$ functions was introduced by Lindenstrauss and Tzafriri and moreover in 2006, the notion of double lacunary sequences was presented by Savaş and Patterson. The primary focus of this article is to introduce the double statistically $\widetilde{\phi }$-convergence and double lacunary statistically $\widetilde{\phi }$-convergence which are generalizations of the double statistically convergence [19] and double lacunary statistically convergence [24]. Additionally, some essential inclusion theorems are examined.