Quantum Difference Relative Uniform Convergence of Double Sequence Spaces of Sargent Type Functions

Resumen

This paper introduces two new double sequence spaces of Sargent type functions, denoted by ₂m(φ,ru,∇_{q}) and ₂n(φ,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}), ℓ_{p}(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.