Geometric Properties and Compact Operator on Fractional Riesz Difference Space

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DOI: 10.46793/KgJMat2304.545Y


In this article we introduce the Riesz difference sequence space rpq(   Bα )
  Δ of fractional order α, defined by the composition of fractional backward difference operator Δ given by (Δv)k = i=0(1)i--Γ (α+1)-
i!Γ (α− i+1)vki and the Riesz matrix Rq. We give some topological properties, obtain the Schauder basis and determine the α-, β- and γ- duals and investigate certain geometric properties of the space rpq(   Bα )
  Δ. Finally, we characterize certain classes of compact operators on the space rpq(      )
  ΔB α using Hausdorff measure of non-compactness.


Riesz difference sequence space, difference operator Δ, geometric properties, Hausdorff measure of non-compactness.


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