Generalized q-Euler Matrix with Associated Sequence Spaces, Duals, and Geometric Properties
Taja Yaying, Bipan Hazarika, S. A. Mohiuddine, Mohsen Rabbani · 2025
We establish a novel regular matrix https://www.w3.org/1998/Math/MathML" display="inline"> E a , b ( q ) , referred to as the q-analogue of the binomial matrix https://www.w3.org/1998/Math/MathML" display="inline"> E a , b . Utilizing the matrix https://www.w3.org/1998/Math/MathML" display="inline"> E a , b ( q ) , we introduce novel BK-spaces https://www.w3.org/1998/Math/MathML" display="inline"> e k ( q ) a , b and https://www.w3.org/1998/Math/MathML" display="inline"> e ∞ ( q ) a , b defined as the domains of https://www.w3.org/1998/Math/MathML" display="inline"> E a , b ( q ) in the spaces https://www.w3.org/1998/Math/MathML" display="inline"> l k and https://www.w3.org/1998/Math/MathML" display="inline"> l ∞ , respectively. Our study encompasses the presentation of various topological characteristics and inclusion relations pertinent to these spaces. We obtain the basis for the space https://www.w3.org/1998/Math/MathML" display="inline"> e k ( q ) a , b and compute the https://www.w3.org/1998/Math/MathML" display="inline"> α -, https://www.w3.org/1998/Math/MathML" display="inline"> β -, and https://www.w3.org/1998/Math/MathML" display="inline"> γ -duals of the spaces https://www.w3.org/1998/Math/MathML" display="inline"> e k ( q ) a , b and https://www.w3.org/1998/Math/MathML" display="inline"> e ∞ ( q ) a , b . Additionally, we derive the requisite conditions, both necessary and sufficient, for a matrix operator to establish a mapping from the spaces https://www.w3.org/1998/Math/MathML" display="inline"> e k ( q ) a , b and https://www.w3.org/1998/Math/MathML" display="inline"> e ∞ ( q ) a , b to any one of the space https://www.w3.org/1998/Math/MathML" display="inline"> l ∞ , https://www.w3.org/1998/Math/MathML" display="inline"> c , c 0 , https://www.w3.org/1998/Math/MathML" display="inline"> l 1 , https://www.w3.org/1998/Math/MathML" display="inline"> b s , c s , c s 0 . Finally, our investigation delves into specific geometric properties related to the space https://www.w3.org/1998/Math/MathML" display="inline"> e k ( q ) a , b .