q-Stirling sequence spaces associated with q-Bell numbers

Abstract

In this study, we build q-analog of the q-Stirling matrix involved q-Bell numbers S-q = (S-nk(q)) defined by S-q = (S-nk(q)) = {(S)(0, otherwise.)(q)(n, k)/B-q(n), 0 <= k <= n, Next, we define the sequence spaces c(S-q), c(0)(S-q), l(infinity) (S-q), l(p)(S-q) (1 <= p < infinity) using this analog. Then, we provide some inclusion relations for these spaces and examine some topological characteristics. Furthermore, we construct a basis for the space l(p)(S-q), calculate alpha-, beta-, gamma-duals of the same space, and describe certain matrix classes.