Quantum Difference Relative Uniform Convergence of Double Sequence Spaces of Sargent Type Functions
Boletim da Sociedade Paranaense de Matematica, cilt.44, sa.7, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 44 Sayı: 7
- Basım Tarihi: 2026
- Doi Numarası: 10.5269/bspm.81541
- Dergi Adı: Boletim da Sociedade Paranaense de Matematica
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Anahtar Kelimeler: BK-space, Double sequence spaces, modular spaces, Quantum difference operator, relative uniform convergence, Sargent-type functions, uniform convexity
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
This paper introduces two new double sequence spaces of Sargent type functions, denoted by 2m(ℱ,ru,∇q) and 2n(ℱ,ru,∇q), which are defined using the concept of relative uniform convergence in combination with the Jackson q-difference operator for double sequences. In this framework, we define bounded, p-absolutely summable, convergent, and null double sequences of functions based on the idea of quantum difference relative uniform convergence with respect to a scale function. These classes are represented by ℓ∞(ru,∇q), ℓp(ru,∇q), 2c(ru,∇q) and 2c0(ru,∇q), respectively. We also explore the inclusion relations and isomorphisms between these newly introduced spaces and other existing function spaces. Additionally, we investigate several algebraic and geometric properties, such as solidness and convexity.