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.

in this study we introduce the concepts of statistical convergence of order$beta$ and strong $p-$ces`{a}ro summability of order $beta$ for sequencesof fuzzy numbers. also, we give some relations between the statisticalconvergence of order $beta$ and strong $p-$ces`{a}ro summability of order$beta$ and construct some interesting examples.

We prove three results concerning convolution operators and lacunary maximal functions associated to dilates of measures. First we obtain an H to L bound for lacunary maximal operators under a dimensional assumption on the underlying measure and an assumption on an Lp regularity bound for some p > 1. Secondly, we obtain a necessary and sufficient condition for L boundedness of lacunary maximal ...

We define lacunary Fourier series on a compact connected semisimple Lie group G. If f ∈ L1(G) has lacunary Fourier series and f vanishes on a non empty open subset of G, then we prove that f vanishes identically. This result can be viewed as a qualitative uncertainty principle.

In this paper we introduced the space of   bounded and   convergent difference sequence of fuzzy soft real numbers and the space of  lacunary   statistically convergent different sequence of fuzzy soft real numbers relating these concepts some theorem are derive. Keyword Fuzzy soft real number,   bounded,   convergent and  lacunary   statistically convergent.