Variations on Rho statistical quasi Cauchy sequences

A sequence (α_k) of points in ℝ, the set of real numbers, is called ρ-statistically p quasi Cauchy if for each ε > 0, where ρ = (ρ_n) is a non-decreasing sequence of positive real numbers tending to ∞ such that $limsupnρnn<∞$⁠, Δρ_n = O(1) and Δ_pα_k+p = α_k+p – α_k for each positive integer k, p is a fixed positive integer. A real-valued function defined on a subset of ℝ is called ρ-statistically p-ward continuous if it preserves ρ-statistical p-quasi Cauchy sequences. We obtain results related to ρ-statistical p-ward continuity, ρ-statistical p-ward compactness, p-ward continuity, ward continuity, and uniform continuity.