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.
Difference operator $\Delta^{\alpha}$ Paranormed sequence space Lacunary sequence Modulus function Multiplier sequence
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Araştırma Makalesi |
Yazarlar | |
Yayımlanma Tarihi | 1 Ekim 2020 |
Gönderilme Tarihi | 29 Mayıs 2020 |
Kabul Tarihi | 23 Ağustos 2020 |
Yayımlandığı Sayı | Yıl 2020 |
This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.