On Lacunary Mean Ideal Convergence in Generalized Randomn-Normed Spaces

Abstract

An idealIis a hereditary and additive family of subsets of positive integersℕ. In this paper, we will introduce the concept of generalized randomn-normed space as an extension of randomn-normed space. Also, we study the concept of lacunary mean (L)-ideal convergence andL-ideal Cauchy for sequences of complex numbers in the generalized randomn-norm. We introduceIL-limit points andIL-cluster points. Furthermore, Cauchy andIL-Cauchy sequences in this construction are given. Finally, we find relations among these concepts.

Stability of Unbounded Differential Equations in Menger k-Normed Spaces: A Fixed Point Technique

“…Definition 2. ( [20,21]) Suppose that * is a ct-norm, S is a linear space and ξ is a mapping from S k to O + . In this case, the ordered tuple (S, ξ, * ) is called a Menger k-normed linear space (in short, M-k-NLS) if the following conditions are satisfied:…”

Lacunary ideal convergence of multiple sequences

“…Hazarika [22] introduced the notion of lacunary ideal convergent double sequences of fuzzy real numbers. Bakery and Mohammed [23] introduced lacunary mean ideal convergence in generalized random n-normed spaces.…”