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

Abstract EN

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.