Some Sequence Spaces Defined by Orlicz Functions

The object of this paper is to introduce a new concept of lacunary strong convergence with respect to an Orlicz function and examine some properties of the resulting sequence spaces. We establish some elementary connections between lacunary strong convergence and lacunary strong convergence with respect to an Orlicz function which satisfies D2-condition. It is also shown that if a sequence is lacunary strongly convergent with respect to an Orlicz function, then it is lacunary statistically convergent. In addition, lacunary strong convergence with respect to an Orlicz function is compared to other summability methods.