On Some Generalized Difference Paranormed Sequence Spaces Associated with Multiplier Sequence Defined by Modulus Function (Analysis in Theory and Applications, 2018)
In this article we introduce the paranormed sequence spaces $( f ,Λ, Δ_m, p)$, $c_0( f ,Λ, Δ_m, p)$ and $l_∞( f ,Λ, Δ_m, p)$, associated with the multiplier sequence $Λ = (λ_k)$, defined by a modulus function $ f$. We study their different properties like solidness, symmetricity, completeness etc. and prove some inclusion results.
Keywords: paranorm; solid space; symmetric space; difference sequence; modulus function; multiplier sequence.