Insights into (λ,μ)-quantum difference relative uniform convergence
Asian-European Journal of Mathematics, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Basım Tarihi: 2026
- Doi Numarası: 10.1142/s1793557126500233
- Dergi Adı: Asian-European Journal of Mathematics
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH
- Anahtar Kelimeler: (λ,μ) convergence, opial property, Quantum difference, relative uniform convergence
- Süleyman Demirel Üniversitesi Adresli: Evet
Özet
This paper presents a new sequence space of functions, denoted as mλ(ϖ,ru,∇q,p), which is defined via (λ,μ)-relative uniform convergence and the Jackson q-difference operator. The space combines aspects of (λ,μ)-convergence, relative uniform convergence, and quantum deformation, shedding light on the interaction between q-calculus and (λ,μ)-averaging. We establish that mλ(ϖ,ru,∇q,p) is a Banach space and satisfies the properties of both BK-spaces and K-spaces when equipped with a q-deformed norm. Further, we explore the geometric properties of this space, including strict convexity, uniform convexity, and the Opial-type condition, all of which depend on the parameters q and (λ,μ). A q-dependent modulus of convexity is formulated, and we establish inclusion relations with classical spaces, such as lp spaces and (λ,μ) difference spaces, including the limiting case as q → 1. These results enrich the theory of sequence spaces and present a unified framework that bridges (λ,μ)-convergence, relative uniform convergence, and quantum calculus.