Study reveals the structure of the generalized quantum difference operator in domains of convergent and null sequences, suggesting isomorphic properties.
In this article, we present a generalization of the kᵗʰ order of forward difference operator Δᵏ using its quantum analog Δᵏq. We study its domains c(Δᵏq) and c₀(Δᵏq) in the spaces c and c₀ of convergent and null sequences, respectively. Additionally, we show that the domains c(Δᵏq) and c₀(Δᵏq) are $BK$-spaces and linearly isomorphic to c and c₀, respectively. Furthermore, we construct Schauder bases and examine the K\"{o}the duals of the spaces c(Δᵏq) and c₀(Δᵏq). The final segment deals with the characterization of certain class of matrix mappings from the spaces c(Δᵏq) and c₀(Δᵏq) to the space ν∈, c₀, _∞,~₁\.
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Toseef Ahmed Malik (2025) studied this question.
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