Sliding window convergence and lacunary statistical convergence for measurable functions via modulus function

Abstract

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.

Seminormed double sequence spaces of four-dimensional matrix and Musielak–Orlicz function

“…Since then in the early part of the last century, many researchers studied this concept and acquired various results, see [ 9 – 11 ]. For more details about sequence spaces and n -normed spaces, see, for instance, [ 17 , 26 , 27 , 31 , 34 – 36 , 41 ] and references therein.…”