On a Generalized Difference Sequence Spaces of Fractional Order associated with Multiplier Sequence Defined by A Modulus Function

Year 2020, Volume: 24 Issue: 5, 1105 - 1114, 01.10.2020

Taja Yayıng

https://doi.org/10.16984/saufenbilder.744881

Abstract

Let Γ(m) denotes the gamma function of a real number m∉{0,-1,-2,…}. Then the difference matrix Δ^α of a fractional order α is defined as
(Δ^α v)_k=∑_i〖(-1)^i (Γ(α+1))/(i!Γ(α-i+1)) v_(k+i) 〗.
Using the difference operator Δ^α, we introduce paranormed difference sequence spaces N_θ (Δ^α,f,Λ,p) and S_θ (Δ^α,f,Λ,p) of fractional orders involving lacunary sequence, θ; modulus function, f and multiplier sequence, Λ=(λ_k). We investigate topological structures of these spaces and examine various inclusion relations.

Keywords

Difference operator $\Delta^{\alpha}$, Paranormed sequence space, Lacunary sequence, Modulus function, Multiplier sequence

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