Lacunary statistical convergence of order beta in difference sequences of fuzzy numbers

Abstract

In this paper, we define the spaces $N_{\theta }^{\beta }\left( p,F,\Delta ^{m}\right) ,$ $S_{\theta }^{\beta }\left( F,\Delta ^{m}\right) ,$ $w_{p}^{\beta }\left( F,\Delta ^{m}\right) $ for sequences of fuzzy numbers using generalized difference operator $\Delta ^{m}$ and a lacunary sequence $\theta $ and give some relations between them, where $ \beta \in \left( 0,1\right] $ and $p>0$. Furthermore, in the last section of paper, some inclusion theorems are presented related to the spaces $ S_{\theta }^{\beta }\left( F,\Delta ^{m}\right) $ and $w_{p}^{\beta }\left( \theta ,f,F,\Delta ^{m}\right) $ according to modulus function $f$.