Some q-fractional order difference sequence spaces

2025/11/06 by Yaying, Taja, Baliarsingh, Pinakadhar, Hazarika, Bipan
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2511.17538

Abstract

This paper intends to develop a q-difference operator ∇^(γ)_q of fractional order γ, and give several intriguing properties of this new difference operator. Our main focus remains on the construction of sequence spaces ℓ_p(∇^(γ)) and ℓ_∞ (∇^(γ)), at the same time comparing these spaces with those already exist in the literature. Apart from obtaining Schauder basis, we determine α-, β-, and γ-duals of the newly defined spaces. A section is also devoted for characterizing matrix classes (ℓ_p(∇^(γ)),\mathfrak X), where \mathfrak X is any of the spaces ℓ_∞, c, c₀ and ℓ₁.

Citations

• On Certain Sequence Spaces

Related

• On some new difference sequence spaces of fractional order
• A class of sequence spaces defined by l-fractional difference operator
• Fractional difference sequence spaces via Pascal mean
• On Some Fractional order Binomial sequence spaces with infinite Matrices
• Fractional ordered Euler Riesz sequence space