On relative uniform convergence of fractional difference sequence of function related to ℓp space

Abstract

In this article, we define the notion of relative uniform convergence of fractional difference sequence of the function space rumϕ(∆ᵅ, p), where p ≥ 0. We established many attributes of rumϕ(∆ᵅ, p), including solidity, symmetry, completeness, convergence-free, sequence algebra, and convex characteristics. The relative uniform fractional difference of p− absolutely summable, bounded, convergent, null sequence of function spaces was also introduced. These are represented by the notations ℓp(∆ᵅru), ℓ∞(∆ᵅru), c(∆ᵅru), c0(∆ᵅru), and their relationship to the space rumϕ(∆ᵅ, p) is reviewed.