Relative uniform convergence of quantum difference sequence of functions related to the ₚ-space

The notion of relative uniform convergence of a sequence of functions was introduced and investigated by Moore, followed by E. W. Chittenden in the twentieth century. The concept attracted the researcher at the beginning, of the twenty-first century. Jackson F. H. initiated the concept of the notion of the quantum difference operator. We introduced the quantum difference sequence space m(φ, ru, ∇ₚ), p≥ 0 of W.L.C. Sargent type. We examine its various properties such as solidity, convergence-free, completeness, etc. Also, some induction results have been established.