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

Abstract

This paper introduces two new double sequence spaces of Sargent type functions, denoted by 2(m)(phi, ru, del(q)) and 2(n)(phi, ru, del(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 ( pound infinity)(ru, del(q)), p(ru pound, del(q)), 2c(0)(ru, del(q)) and 2c(0)(ru, del(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.