Quantum Difference Relative Uniform Convergence of Double Sequence Spaces of Sargent Type Functions
Boletim da Sociedade Paranaense de Matematica, vol.44, no.7, 2026 (ESCI, Scopus)
- Publication Type: Article / Article
- Volume: 44 Issue: 7
- Publication Date: 2026
- Doi Number: 10.5269/bspm.81541
- Journal Name: Boletim da Sociedade Paranaense de Matematica
- Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Keywords: BK-space, Double sequence spaces, modular spaces, Quantum difference operator, relative uniform convergence, Sargent-type functions, uniform convexity
- Süleyman Demirel University Affiliated: Yes
Abstract
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.