In this paper, we generalize the concept of I statistical convergence, which is a recently introduced summability method, with an in…nite matrix of complex numbers and a modulus function. Lacunary sequences will also be included in our de…nitions. The name of our new method will be AI -lacunary statistical convergence with respect to a sequence of modulus functions. We also de…ne strongly AI -l...

In this paper‎, ‎following a very recent‎ ‎and new approach‎, ‎we further generalize recently introduced‎ ‎summability methods‎, ‎namely‎, ‎$I$-statistical convergence and‎ ‎$I$-lacunary statistical convergence (which extend the important‎ ‎summability methods‎, ‎statistical convergence and lacunary‎ ‎statistical convergence using ideals of $mathbb{N}$) and‎ ‎introduce the notions of $I$-statis...

1. Statement of the principal result. The class of sequences obtainable as Fourier coefficients of measures on the circle group presents numerous structure problems of interest. Amongst the earliest results somewhat akin to that stated below appear Banach's theorems about lacunary coefficients; see e.g., [4, pp. 215-220]. More recently Helson [3] has studied analogous questions when the group c...

In this paper we purpose to define the notions of lacunary statistical convergence and lacunary statistically Cauchy in random 2-normed spaces and proved some interesting results for these concepts in this set up.

In this paper we introduce the concepts of double lacunary strongly convergence and double lacunary statistical convergence of double interval numbers. We prove some inclusion relations and study some of their properties. Subjclass [2000] : 40C05,40J05, 46A45.