This study is about neutrosophic structures, which one of the popular topics recent days. In this study, different types convergence concepts were applied to difference sequences. With help properties double type sequences, concept sequences combined with structures that are advantageous work like Lacunary

1. Fundamental theorem. In a recent paper f I have proved the theorem that if a lacunary trigonometric series CO (1) X(a* cos nk6 + bk sin nk9) (nk+x/nk > q > 1, 0 ^ 0 ^ 2ir) 4-1 has its partial sums uniformly bounded on a set of 0 of positive measure, then the series (2) ¿(a*2 + bk2) k-l converges. The proof was based on the following lemma (which was not stated explicitly but is contained in ...

We obtain new upper bounds on the number of distinct roots lacunary polynomials over finite fields. Our focus will be for which there is a large gap between consecutive exponents in monomial expansion.

Given an integer matrix M ∈ GLn(R) and a point y ∈ R/Z, consider the set Ẽ(M,y) def = { x ∈ R : y / ∈ {Mkx mod Zn : k ∈ N} } . S.G. Dani showed in 1988 that whenever M is semisimple and y ∈ Q/Z, the set Ẽ(M,y) is winning in the sense of W. Schmidt (a property implying density and full Hausdorff dimension). In this paper we strengthen this result, extending it to arbitrary y ∈ R/Z and M ∈ GLn(R)...

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...

Nanda 1 studied sequence of fuzzy numbers and showed that the set of all convergent sequences of fuzzy numbers form a complete metric space. Nuray 2 proved the inclusion relations between the set of statistically convergent and lacunary statistically convergent sequences of fuzzy numbers. Kwon and Shim 3 studied statistical convergence and lacunary statistical convergence of sequences of fuzzy ...

A blend of matrix summability and Euler transformation methods is used to define Lacunary sequence spaces defined over n-normed space. Then we present the properties this space finally, some inclusion relations are presented.