Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu
We prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.