By a classical result of Weyl (1916), for any increasing sequence (nk) of positive integers, (nkx) is uniformly distributed mod 1 for almost all x. The precise asymptotics of the discrepancy of this sequence is known only in a few cases, e.g. for nk = k (Khinchin (1924)) and for lacunary (nk) (Philipp (1975)). In this paper we extend Philipp’s result to lacunary sequences with multidimensional ...

In this paper we study the concept of asymptotically double lacunary statistical convergent sequences in probabilistic normed spaces and prove some basic properties.

In this study, as a new approach to the concept of asymptotical equivalence in Wijsman sense for double set sequences, concepts which are called invariant statistical order ? and lacunary (0<??1) sequences introduced explained with examples. addition, existence some relations between these furthermore, relationships previously studied investigated.

The purpose of this paper is to define and study the spaces [ĉ,M, p](∆u , q, s), [ĉ,M, p, ] θ 0(∆ m u , q, s) and [ĉ,M, p, ] θ ∞(∆ m u , q, s) of lacunary convergent sequences. We also study some inclusion relations between these spaces and some properties and theorems. 2000 Mathematics Subject Classification:40D05, 40A05. 1.Introduction and definitions Let w denote the set of all complex seque...

By a classical principle of probability theory, sufficiently thin subsequences of general sequences of random variables behave like i.i.d. sequences. This observation not only explains the remarkable properties of lacunary trigonometric series, but also provides a powerful tool in many areas of analysis, such the theory of orthogonal series and Banach space theory. In contrast to i.i.d. sequenc...

In this paper we introduce and study lacunary statistical convergence for double sequences of fuzzy numbers and we shall also present some inclusion theorems.

Based on the concept of lacunary statistical convergence sequences fuzzy numbers, convergence, uniformly and equi-lacunary double fuzzy-valued functions are defined investigated in this paper. The relationship among functions, their representations ? -level cuts discussed. In addition, we obtain form Egorov’s theorem for...