The purpose of this paper is to introduce the concepts of lacunary almost statistical limit and cluster points of sequences of fuzzy numbers. For any lacunary sequence = ( ); and for any sequence = ( ) of fuzzy numbers, we introduce new sets: Λ ( ), Γ ( ),Λ ̂ ( ),Γ ( ) and obtain some relations between these sets.

We call a finitely generated group lacunary hyperbolic if one of its asymptotic cones is an R-tree. We characterize lacunary hyperbolic groups as direct limits of Gromov hyperbolic groups satisfying certain restrictions on the hyperbolicity constants and injectivity radii. Using central extensions of lacunary hyperbolic groups, we solve a problem of Gromov by constructing a group whose asymptot...

This paper presents the following definition which is a natural combination of the definition for asymptotically equivalent, statistically limit and lacunary sequences. Let θ be a lacunary sequence; the two nonnegative sequences x = (xk) and y = (yk) are said to be asymptotically ∆ m lacunary statistical(defined in [2]) equivalent of multiple L provided that for every > 0, lim r 1 hr { the numb...

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 article we introduce and study the notions of double -lacunary strongly summable, double  Cesàro strongly summable, double  statistically convergent and double  -lacunary statistically convergent sequence of fuzzy numbers. Consequently we construct the spaces   2 F L  ,   2 F   ,   2 F S  and   2 F S  respectively and investigate the relationship among these spaces. F...

In the present paper, we study the geometric discrepancy with respect to families of rotated rectangles. The well-known extremal cases are the axis-parallel rectangles (logarithmic discrepancy) and rectangles rotated in all possible directions (polynomial discrepancy). We study several intermediate situations: lacunary sequences of directions, lacunary sets of finite order, and sets with small ...

In this paper, we present a new method for computing boundeddegree factors of lacunary multivariate polynomials. In particular for polynomials over number fields, we give a new algorithm that takes as input a multivariate polynomial f in lacunary representation and a degree bound d and computes the irreducible factors of degree at most d of f in time polynomial in the lacunary size of f and in ...

We develop a local theory of lacunary Dirichlet series of the form ∞