A New Generalization of the Hahn Sequence Space via Speed Sequences λ = λk

This paper investigates the properties and structural characteristics of the new Hahn sequence space defined through the speed sequence λ = (λk). First, we define the new Hahn sequence space h(λ) with speed, where the speed sequence λ = (λk) is an unbounded monotone increasing sequence of positive real numbers. Then, we study some topological properties of the space h(λ). Moreover, we show some inclusion relations pertaining to the space h(λ) and calculate the α − , β−, and γ−dual of the space h(λ). Finally, we complete the paper with some matrix transformations from h(λ) into μ, where μ∈c0,c,l∞,l1,h,bv,bvp,bv∞,bs,cs,cs0, and from the space γ into h(λ), where γ∈c0,c,l∞,l1,h,bv,bv0,bs,cs,cs0.