Abstract
In this study, we introduce newBK-spacesbsr,tp,qandb∞r,tp,qderived by the domain ofp,q-analogueBr,tp,qof the binomial matrix in the spacesℓsandℓ∞,respectively. We study certain topological properties and inclusion relations of these spaces. We obtain a basis for the spacebsr,tp,qand obtain Köthe-Toeplitz duals of the spacesbsr,tp,qandb∞r,tp,q.We characterize certain classes of matrix mappings from the spacesbsr,tp,qandb∞r,tp,qto spaceμ∈ℓ∞,c,c0,ℓ1,bs,cs,cs0.Finally, we investigate certain geometric properties of the spacebsr,tp,q.
Highlights
Introduction and PreliminariesThe ðp, qÞ-calculus has been a wide and interesting area of research in recent times
In the field of mathematics, it is widely used by researchers in operator theory, approximation theory, hypergeometric functions, special functions, quantum algebras, combinatorics, etc
QÞ-analogue of a known mathematical expression, we mean the generalization of that expression using two independent variables p and q rather than a single variable q as in q-calculus
Summary
The ðp, qÞ-calculus has been a wide and interesting area of research in recent times. We introduce sequence spaces bsr,tðp, qÞ and b∞ r,t ðp, qÞ, study their topological properties and some inclusion relations, and obtain a basis for the space bsr,tðp, qÞ: Let r, t be nonnegative real numbers and 0 < q < p ≤ 1 holds, the generalized ðp, qÞ-Euler matrix Br,tðp, qÞ =. Talebi [25] obtained Köthe-Toeplitz duals of the domain of an arbitrary invertible summability matrix in ls space We follow his approach to find the KötheToeplitz duals of the spaces bsr,tðp, qÞ and br∞,t ðp, qÞ: In the rest of the paper, N will denote the family of all finite subsets of N0 and k = s/1 − s is the complement of s: Theorem 12.
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