Weak convergence of sequences defined by Orlicz function in n-normed space

Abstract

In this article, we investigate the weak convergence of sequences defined by Orlicz functions
within the framework of n-normed spaces. The concept of Orlicz sequence spaces, which generalize classical ℓ_p
spaces, provides a flexible structure for analyzing sequence behavior through convex functions. On the other
hand, n-normed spaces, originally introduced by Gähler, extend the notion of norm by considering n-tuples
of vectors, offering a rich setting for functional analysis. We introduce and study a new classes of weakly
convergent sequences in Orlicz sequence spaces under the n-norm We have explained its different algebraic
and topological properties, We have also proved the geometric properties of these sequence spaces.