On Lacunary Mean Ideal Convergence in Generalized Random n-Normed Spaces - Awad A. Bakery; Mustafa M. Mohammed (Abstract and Applied Analysis)
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 IL-limit points and IL-cluster points. Furthermore, Cauchy and IL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.