In this article we introduce the concepts of lacunary Iconvergent sequences. We investigate its different properties like solid, symmetric, convergence free etc.

In this paper, we define the space Sαθ (∆mv, f) of all f)-lacunary statistical convergent sequences order α with help unbounded modulus function f, lacunary sequence (θ), generalized difference operator ∆ mv and real number ∈ (0, 1]. We also introduce ωαθ strong summable α. Properties related to these spaces are studied. Inclusion relations between ωα θ established under certain conditions.

Recently, Mohiuddine and Alghamdi introduced the notion of lacunary statistical convergence in a locally solid Riesz space and established some results related to this concept. In this paper, some inclusion relations between the sets of statistically convergent and lacunary statistically convergent sequences are established and extensions of a decomposition theorem, a Tauberian theorem to the l...

The sequence X = {Ark } of fuzzy numbers is statistically convergent to the fuzzy number 3(o provided that for each e ~ 0 lim l{the number ofk~e} = 0. n In this paper we study a related concept of convergence in which the set {k: k<~n} is replaced by {k: kr-1 -~k<~kr} for some lacunary sequence {k~}. Also we introduce the concept of lacunary statistically Cauchy sequence and show...

A lacunary sequence is an increasing integer sequence θ = {kr } such that kr − kr−1 → ∞ as r → ∞. A sequence x is called sθ-convergent to L provided that for each ε > 0, limr (1/(kr −kr−1)){the number of kr−1 < k ≤ kr : |xk−L| ≥ ε} = 0. In this paper, we study the general description of inclusion between two arbitrary lacunary sequences convergent.

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.

In this article, we introduce the lacunary difference sequence spaces w0(M , θ,∆ n m, p, q), w1(M , θ,∆ n m, p, q) and w∞(M , θ,∆ n m, p, q) using a sequence M = (Mk) of Orlicz functions and investigate some relevant properties of these spaces. Then, we define and study the notion of qlacunary ∆nm-statistical convergent sequences. Further, we study the relationship between q-lacunary ∆nm-statis...

(1) On page 529: The statement “we will denote the set of all double lacunary sequences by Nθr,s ” should be removed. (2) On page 529: In Definition 2.4, the statement “for every ε > 0” should be removed. (3) On page 530: In the proof of (C), for all K should be replaced with for all k and l. (4) The references “Li, J. Lacunary statistical convergence and inclusion properties between lacunary m...

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 ...