The main object of this paper is to introduce and study a new concept of f-Wijsman lacunary statistical convergence of sequences of sets, where f is an unbounded modulus. The definition of Wijsman lacunary strong convergence of sequences of sets is extended to a definition of Wijsman lacunary strong convergence with respect to a modulus for sequences of sets and it is shown that, under certain ...

Introduction This paper tries to shed some light on the very classical topic of overconvergence for Dirichlet series, by employing results in the theory of innite order dier-ential operators with constant coecients ([3], [13]). The possibility of linking innite order dierential operators with gap theorems and related subjects such as overconvergence phenomena was rst suggested by Ehrenpreis in ...

We show that if f(z) = ∑ anz n is a holomorphic function in the Dirichlet space of the unit disk, then almost all of its randomizations ∑ ±anz are multipliers of that space. This parallels a known result for lacunary power series, which also has a version for smoothness classes: every lacunary Dirichlet series lies in the Lipschitz class Lip1/2 of functions obeying a Lipschitz condition with ex...

The aim of present work is to introduce and study lacunary statistical limit and lacunary statistical cluster points for generalized difference sequences of fuzzy numbers. Some inclusion relations among the sets of ordinary limit points, statistical limit points, statistical cluster points, lacunary statistical limit points, and lacunary statistical cluster points for these type of sequences ar...

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.

The solution chemistry of a series of mono-, di- and trilacunary Keggin silicotungstates was investigated by electrospray ionization mass spectrometry (ESI-MS) and general electrospray features especially for lacunary POMs are summarized. The reactions of vanadium incorporation into the lacunary structures were successfully monitored in real-time by a combination of ESI-MS and differential puls...

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...