The Chebyshev theory of a variation of \(L\) approximation (Q1180588)

The author proposes a method of approximation of continuous functions on \([a,b]\) with respect to the norm \(\parallel f \parallel :=sup\{ \mid \int^ d_ cf(x)dx \mid :a\leq c \leq d \leq b\}\) and shows that such an approximation maintains almost all of the essentials of the Chebyshev theory of best uniform approximation, while also using an \(L\)-type measure of approximation.