Exploring the Z-Spaces of Double Sequences of Scalars: Z2-Spaces
Journal of Mathematics, vol.2026, no.1, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 2026 Issue: 1
- Publication Date: 2026
- Doi Number: 10.1155/jom/7268682
- Journal Name: Journal of Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Keywords: double sequence spaces, multiplier spaces, weighted means, Z(2)-spaces, β-duals
- Ondokuz Mayıs University Affiliated: Yes
Abstract
In this paper, we introduced and investigated the spaces (Formula presented.) of double sequences as natural extensions of the classical sequence spaces (Formula presented.). We characterized the β-duals of these spaces and obtained explicit representations in terms of multiplier spaces and difference-type conditions involving the operators (Formula presented.). Furthermore, we examined the relationships between weighted mean methods and the β-duals of certain special cases of (Formula presented.). Several illustrative examples are provided to clarify the structure of the introduced spaces and to demonstrate the applicability of the obtained results. The results presented here generalize a number of known results on (Formula presented.) -spaces from the setting of ordinary sequences to double sequences.