Here, we continued the studies initiated by Vinod K. Bhardwaj and Shweta Dhawan which relate different convergence methods involving classical statistical strong Cesàro convergences means of lacunary sequences measures density in N modulated a modulus function f. A method for constructing non-compatible functions was also included, is related to symmetries with respect y=x.

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 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 ...

Marouf (1993) presented definitions for asymptotically equivalent sequences and asymptotic regular matrices. Patterson (2003), extended those concepts by presenting an asymptotically statistical equivalent analog of these definitions and natural regularity conditions for non-negative sum ability matrices. In Patterson and Savas (2006) extended the definitions presented in (Patterson, 2003) to l...

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 .

A lacunary sequence is an increasing integer sequence θ = (kr) such that k0 =0, kr−kr−1 →∞ as r →∞. A sequence x is called Sθ(∆)− convergent to L provided that for each ε > 0, limr(kr − kr−1) {the number of kr−1 < k ≤ kr : |∆xk−L| ≥ ε} = 0, where ∆xk = ∆xk− ∆xk+1. The purpose of this paper is to introduce the concept of ∆ − lacunary statistical convergence and ∆-lacunary strongly convergence an...