On the New Generalized Hahn Sequence Space hdp. (16th September 2022)

• Record Type: Journal Article
• Authors: Tuğ, Orhan; Malkowsky, Eberhard; Hazarika, Bipan; Yaying, Taja
• Other Names: Giné Jaume Academic Editor.
• Is Part Of: Abstract and applied analysis. Volume 2022(2022)
• Publication Date: 2022-09-16
• Subjects: Mathematical analysis -- Periodicals; Mathematical analysis; Applied Mathematics; Mathematical Analysis; Periodicals; 515.05
• DOI: 10.1155/2022/6832559
• Languages: English
• ISSNs: 1085-3375

Abstract

Abstract : In this article, we define the new generalized Hahn sequence space h d p, where d = d k k = 1 ∞ is monotonically increasing sequence with d k ≠ 0 for all k ∈ ℕ, and 1 < p < ∞ . Then, we prove some topological properties and calculate the α −, β −, and γ − duals of h d p . Furthermore, we characterize the new matrix classes h d, λ, where λ = b v, b v p, b v ∞, b s, c s, , and μ, h d, where μ = b v, b v 0, b s, c s 0, c s . In the last section, we prove the necessary and sufficient conditions of the matrix transformations from h d p into λ = ℓ ∞, c, c 0, ℓ 1, h d, b v, b s, c s, and from μ = ℓ 1, b v 0, b s, c s 0 into h d p .