In this paper, using the fractional difference operator and a modulus function we introduce concepts of $({}^{}_{2}{\Delta_{\beta}^{\tilde{\alpha}}},f)-$ statistical convergence, $({}^{}_{2}{\Delta^{\tilde{\alpha}}},f)-$ Cauchy p-strongly Cesàro summability, $(0<p<\infty)$ for double sequences. We also give some inclusion relations between convergence summability $(0<p<\infty)$.

In this paper, we present statistical weighted mean ( briefly, (N?,p,q,1,1)) summability method for double sequences of fuzzy numbers and give necessary sufficient Tauberian conditions under which convergence a sequence follows from its (N?,p,q,1,1) summability. Furthermore, apply our new to prove Korovkin type approximation theorem positive linear operators.

the goal of this paper is to generalize the recently introduced summability method and introduce double statistical convergence of order  by using ideal. we also investigate certain properties of this convergence.

In this article we introduce the notion of different types of statistically convergent and statistically null fuzzy real-valued double sequence spaces. We study their different properties like solidness, symmetric, convergence free, sequence algebra etc. The fuzzy real-valued Cesàro summable double sequence space is introduced. A relation between strongly p-Cesàro summability and bounded statis...

*Correspondence: [email protected] Department of Mathematics, İstanbul Commerce University, Sütlüce/Beyoğlu, İstanbul, Turkey Abstract Das (Proc. Camb. Philos. Soc. 67:321-326, 1970) proved that every conservative Hausdorff matrix is absolutely kth power conservative. Savaş and Rhoades (Anal. Math. 35:249-256, 2009) proved the result of Das for double Hausdorff summability. In this paper we...

In this paper, we study the concepts of Wijsman Cesàro summability and Wijsman lacunary convergence of double sequences of sets and investigate the relationship between them.