### 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, r

_{0}

^{t}, r

_{c}

^{t}and r

_{∞}

^{t}deﬁned by the composition of fractional diﬀerence operator Δ

^{(α)}, deﬁned by (Δ

^{(α)}x)

_{k}= ∑

_{i=0}

^{∞}(−1)

^{i}x

_{k−i}, and Riesz mean matrix R

^{t}. 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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