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


Demirci I. A., Kişi Ö., GÜRDAL M.

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.