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

Abstract

Let Γ(𝑚) denotes the gamma function of a real number 𝑚 ∉ {0, −1, −2, … }. Then the difference matrix Δa of a fractional order 𝛼 is defined as Using the difference operator Δa , we introduce paranormed difference sequence spaces 𝑁ఏ(Δఈ 𝑓, Λ, 𝑝) and 𝑆ఏ(Δఈ, 𝑓, Λ, 𝑝) of fractional orders involving lacunary sequence, 𝜃; modulus function, 𝑓 and multiplier sequence, Λ = (𝜆). We investigate topological structures of these spaces and examine various inclusion relations.Keywords: Difference operator Δa , Paranormed sequence space, Lacunary sequence, Modulus function, Multiplier sequence.