Orlicz-Garling sequence spaces of difference operator and their domination in Orlicz-Lorentz spaces.

We introduce new classes of generalized Orlicz-Garling sequences and Orlicz-Lorentz sequences by using a sequence of Orlicz functions and difference operator. We show that the Orlicz-Garling sequence space admits a unique 1-subsymmetric basis and a 1-dominated block basic sequence in [Formula: see text]. We also make an effort to prove that every symmetric normalized block Orlicz-Garling sequence dominates an Orlicz-Lorentz sequence. Finally, we study some geometric properties of these spaces and establish some inclusion relations between spaces.

Seminormed double sequence spaces of four-dimensional matrix and Musielak-Orlicz function.

In this paper we study seminormed double sequence spaces of a four-dimensional matrix and Musielak-Orlicz function over n-normed spaces. We explore some interesting inclusion relations, algebraic and topological properties of these spaces.

On generalized difference Hahn sequence spaces.

We construct some generalized difference Hahn sequence spaces by mean of sequence of modulus functions. The topological properties and some inclusion relations of spaces h p ((F, u, Δ(r)) are investigated. Also we compute the dual of these spaces, and some matrix transformations are characterized.