In this paper we study the concepts of sliding window convergence for real valued measurable functions dened on [0,1) via modulus function. We also establish some inclusions and consistency theorems for sequential methods along with examples. Finally, we give a Cauchy convergence criterion.
In the paper [32], we have defined the concepts of lacunary statistical
convergence of order ? and strong N?(p)-summability of order ? for
sequences of complex (or real) numbers. In this paper we continue to examine
others relations between lacunary statistical convergence of order ? and
strong N?(p)-summability of order ?.
Some spaces of difference sequences and lacunary statistical convergence in $n$-normed space defined by sequence of Orlicz functions
