On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces

Abstract

An ideal $I$ is a hereditary and additive family of subsets of positive integers $\mathbb{N}$. In this paper, we will introduce the concept of generalized random $n$-normed space as an extension of random $n$-normed space. Also, we study the concept of lacunary mean ($L$)-ideal convergence and $L$-ideal Cauchy for sequences of complex numbers in the generalized random $n$-norm. We introduce $I_L$-limit points and $I_L$-cluster points. Furthermore, Cauchy and $I_L$-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.