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 ...

This paper presents new definitions which are a natural combination of the definition for asymptoticall equivalence and ∆−statistical convergence of sequences. Let θ = (k r) be a lacunary sequence. Then the sequences x and y are said to be [w] L θ,∆ −asymptotically equivalent of multiple L provided that for every ε > 0 lim r 1 h r k ∈ I r : t km (∆x k) t km (∆y k) − L ≥ ε = 0 .

In earlier works, F. León and coworkers discovered a remarkable structure between statistical convergence strong Cesàro convergence, modulated by function f (called modulus function). Such nice pivots around the notion of compatible function. this paper, we will explore such in framework lacunary for double sequences discover that remains true functions. Thus, continue work Hacer Şenül, Mikail ...

In this paper our purpose is to extend some results known in the literature for ordinary difference (single) to difference double sequences of real numbers.Quite recently, Esi [1] defined the statistical analogue for double difference sequences x = (xk,l) as follows: A real double sequence x = (xk,l) is said to be P-statistically ∆− convergent to L provided that for each ε > 0 P − lim m,n 1 mn ...

In this paper, we study the concepts of lacunary statistical convergent and lacunary statistical Cauchy sequences in probabilistic normed spaces and prove some basic properties.