@article{article_744881, title={On a Generalized Difference Sequence Spaces of Fractional Order associated with Multiplier Sequence Defined by A Modulus Function}, journal={Sakarya University Journal of Science}, volume={24}, pages={1105–1114}, year={2020}, DOI={10.16984/saufenbilder.744881}, author={Yayıng, Taja}, keywords={Difference operator $\Delta^{\alpha}$, Paranormed sequence space, Lacunary sequence, Modulus function, Multiplier sequence}, 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.}, number={5}, publisher={Sakarya University}