ON f− STATİSTİCAL CONVERGENCE OF FRACTİONAL DİFFERENCE ON DOUBLE SEQUENCES

Abstract

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