Generalized Difference Sequence Spaces of Fractional Order Defined by Orlicz Functions

Abstract

The main purpose of this paper is to introduce the concepts of lacunary statistical convergence of order (0 < 1) with the fractional order of and lacunary strongly convergence of order (0 < 1) with the fractional order of. We establish some connections between lacunary strongly convergence of order and lacunary statistical convergence of order .

A Note on Lacunary Sequence Spaces of Fractional Difference Operator of Orderα,β

“…For details about nnormed spaces, we refer to ( [51][52][53][54][55]), difference sequence spaces ( [38,39]), Orlicz function ( [56][57][58]). Ideal convergence and fractional difference operator Δ α has been studied in [59,60]. We continue in this connection and construct new sequence spaces as follows.…”

On ρ-statistical convergence of order α of sequences of sets

“…Schoenberg [28] established some basic properties of statistical convergence and studied the concept as a summability method. Later on it was further investigated from the sequence space point of view and linked with summability theory by Altınok et al [1], Aral et al ( [2,3]), Bhardwaj and Dhawan [5], C ¸akallı et al ( [6][7][8]), Caserta et al [9], C ¸ınar et al [10], Connor [12], C ¸olak [11], Demirci et al [13], ), Fridy [19], Gadjiev and Orhan [20], Is ¸ık and Akbas ¸ [21], Salat [26], Savas and Et [27], S ¸engül [29] and many others. Let (X, σ) be a metric space.…”