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

Authors : Taja YAYING

Pages : 1105-1114

Doi:10.16984/saufenbilder.744881

View : 24 | Download : 21

Publication Date : 2020-10-01

Article Type : Research Paper

Abstract :Let Γinsert ignore into journalissuearticles values(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 insert ignore into journalissuearticles values(Δ^α v);_k=∑_i〖insert ignore into journalissuearticles values(-1);^i insert ignore into journalissuearticles values(Γinsert ignore into journalissuearticles values(α+1););/insert ignore into journalissuearticles values(i!Γinsert ignore into journalissuearticles values(α-i+1);); v_insert ignore into journalissuearticles values(k+i); 〗. Using the difference operator Δ^α, we introduce paranormed difference sequence spaces N_θ insert ignore into journalissuearticles values(Δ^α,f,Λ,p); and S_θ insert ignore into journalissuearticles values(Δ^α,f,Λ,p); of fractional orders involving lacunary sequence, θ; modulus function, f and multiplier sequence, Λ=insert ignore into journalissuearticles values(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