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

An ideal I is a hereditary and additive family of subsets of positive integers 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.