The main aim of this article is to generalize the notion of almost convergent, Cesàro summable and lacunary summable spaces by using a generalized difference operator defined associating a sequence of non-zero scalars and characterize some matrix classes involving these sequence spaces. In this article we also introduce the idea of difference infinite matrices. It is expected that these investi...

In the present paper we introduce some vector-valued multiplier difference sequence spaces defined by a Musielak-Orlicz function, concepts of lacunary convergence and strong (A, u)-convergence, where A = (aik) is an infinite matrix of complex numbers and u = (ui) be any sequence of strictly positive real numbers. We also make an effort to study some topological properties and some inclusion rel...

In this article we introduce the notion of lacunary statistically convergent and lacunary statistically Cauchy sequences in intuitionistic fuzzy n-normed linear spaces and give their characterization. We show that some properties of lacunary statistical convergence of real sequences also hold for sequences in this space. Further, necessary and sufficient conditions for equality of the set of st...

We show how wavelet techniques allow to derive irregularity properties of functions on two particular examples: Lacunary Fourier series and some Gaussian random processes. Then, we work out a general derivation of the multifractal formalism in the sequence setting, and derive some of its properties.

For any lacunary sequence θ = (kr), the aim of the present work is to introduce strong θ-statistical limit and strong θ-statistical cluster points of sequences on probabilistic normed spaces (briefly PN-spaces). Some relations among the sets of ordinary limit points, strong θ-statistical limit and strong θ-statistical cluster points of sequences on PN-spaces are obtained.

An example due to Erdős and Fortet shows that, for a lacunary sequence of integers (qn) and a trigonometric polynomial φ, the asymptotic distribution of 1 √ n ∑n−1 k=0 φ(qkx) can be a mixture of gaussian laws. Here we give a generalization of their example interpreted as the limiting behavior of some modified ergodic sums in the framework of dynamical systems.

In this article, we have introduced the idea of statistically convergent generalized difference lacunary double sequence spaces 2 [ ( , , , )] n w M p q θ Δ , 2 0 [ ( , , , )] n w M p q θ Δ and defined over a semi norm space (X, q). Also we have study some basic properties and obtained some inclusion relations between them.

We introduce the sequence spaces [ ˆ w(M)] and [ ˆ w(M)] θ of strong almost convergence and lacunary strong almost convergence respectively defined by the Orlicz function M. We establish certain inclusion relations and show that the above spaces are same for any bounded sequences. 1. Definitions and notations A sequence x ∈ l ∞ , the space of bounded sequences x = (x k), is said to be almost co...