On lacunary mean ideal convergence in generalized random \(n\)-normed spaces
Summary: 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.
scientific article; zbMATH DE number 7021733
scientific article