The Generalized quantum difference operator in c and c_0 and their duals - Malik, Toseef Ahmed (Sarajevo Journal of Mathematics, 2025)
In this article, we present a generalization of the k^th order of forward difference operator Δ^k using its quantum analog Δ^k_q. We study its domains c(Δ^k_q) and c_0(Δ^k_q) in the spaces c and c_0 of convergent and null sequences, respectively. Additionally, we show that the domains c(Δ^k_q) and c_0(Δ^k_q) are BK-spaces and linearly isomorphic to c and c_0, respectively. Furthermore, we construct Schauder bases and examine the K"othe duals of the spaces c(Δ^k_q) and c_0(Δ^k_q). The final segment deals with the characterization of certain class of matrix mappings from the spaces c(Δ^k_q) and c_0(Δ^k_q) to the space u{c, c_0, _∞, _1}.