The New Hahn Sequence Space via $(p,q)$-Calculus - Serkan Demiriz; Sezer Erdem; Hacer Bilgin Ellidokuzoğlu (Communications in Advanced Mathematical Sciences)
In this paper, a novel generalized Hahn sequence space, denoted as $h(C(p,q))$, is introduced by utilizing the $(p, q)$-Cesaro matrix. Fundamental properties of this sequence space, such as its completeness and inclusion relations with other well-known sequence spaces, are explored. The duals of this newly constructed sequence space are also determined, providing insights into its structural and functional characteristics. Furthermore, matrix mapping classes of the form $(h(C(p,q)):μ)$ are characterized for various classical sequence spaces $μ \in \{c_0, c, \ell_∞, \ell_1, h\}$, extending the applicability of the proposed space to broader mathematical contexts. The results obtained contribute to the ongoing development of sequence space theory and its applications in functional analysis.