Paranormed Riesz Difference Sequence Spaces of Fractional Order


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Authors: T. YAYING

DOI: 10.46793/KgJMat2202.175Y

Abstract:

In this article we introduce paranormed Riesz difference sequence spaces of fractional order α, r0t(     (α))
 p, Δ, rct(     (α))
 p, Δ and rt(      (α))
  p,Δ defined by the composition of fractional difference operator Δ(α), defined by (Δ(α)x)k = i=0(1)i Γ (α+1 )
i!Γ (α−-i+1-)xki, and Riesz mean matrix Rt. We give some topological properties, obtain the Schauder basis and determine the α-, β- and γ- duals of the new spaces. Finally, we characterize certain matrix classes related to these new spaces.



Keywords:

Riesz difference sequence spaces, difference operator Δ(α), Schauder basis, α-, β-, γ- duals, matrix transformation.



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