Approximation of functions of finite generalized variation by rational functions (Q788223)

In this paper, the author obtains upper and lower bounds for the best rational approximation on [a,b]\(\subset {\mathbb{R}}\) in the mean p, \(0<p<\infty\), of the class of measurable functions f on [a,b] such that \(\sup \{\sum^{n-1}_{k=0}\Phi(| f(x_{k+1})-f(x_ k)|)\}\leq M\) where the supremum is taken over the class of all possible partitions of [a,b], \(\Phi\) is an increasing continuous and concave function on \([0,\infty [\) and \(M>0\).