Waterman Classes and Piecewise Monotone Approximations / A.N. Bakhvalov // Vestn. Mosk. Univ., Matem. Mekhan. 2009. № 6. P. 46-48 [Moscow Univ. Math. Bulletin. Vol. 64, No 6, 2009. P. 259-261.]
We obtain a necessary and sufficient condition for a class of functions with a given estimate of the decreasing rate of their piecewise monotone approximations to be embedded into the Waterman class (the class of functions with bounded Λ-variation).
Key words: piecewise monotone approximation, genezalized variation.