On the New Generalized Hahn Sequence Space hpd

Tuğ, Orhan and Malkowsky, Eberhard and Hazarika, Bipan and Yaying, Taja (2022) On the New Generalized Hahn Sequence Space hpd. Abstract and Applied Analysis, 2022.

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Abstract

In this article, we define the new generalized Hahn sequence space h p d, where d = ðdkÞ ∞ k=1 is monotonically increasing sequence with dk ≠ 0 for all k ∈ ℕ, and 1 < p < ∞. Then, we prove some topological properties and calculate the α − , β − , and γ − duals of h p d. Furthermore, we characterize the new matrix classes ðhd, λÞ, where λ = fbv, bvp, bv∞, bs, cs,g, and ðμ, hdÞ, where μ = fbv, bv0, bs, cs0, csg. In the last section, we prove the necessary and sufficient conditions of the matrix transformations from h p d into λ = fℓ∞, c, c0, ℓ1, hd, bv, bs, csg, and from μ = fℓ1, bv0, bs, cs0g into h p d.

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