The object of this paper is to introduce the sequence space ces(f, p) using a modulus function f. Various algebraic and topological properties of this space, and certain inclusion relations have been discussed which generalize several known results of Shiue [10], Sanhan and Suantai [9], and Leibowitz [2].
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The main purpose of this paper is to introduce a new concept of [...]-lacunary statistical convergence. It is shown that if a sequence is [...]-lacunary strongly summable with index p with respect to an Orlicz function M then it is A [...]-lacunary statistically convergent and that the concepts of [...]-lacunary strong summability with index p with respect to an Orlicz function M and [...]-lacunary statistical convergence are equivalent on [...]-bounded sequences. The composite space no [...] using composite Orlicz function Mv has also been introduced. It is also shown that if q is total, then every [...] method is consistent with the W[...] method. Our results generalize and unify the corresponding earlier results of Freedman et al. [5], Tripathy et al. [17, 18, 19] and, Bhardwaj and Singh [1].
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