Global Estimates for Monotone Approximation

Abstract

In 1995 Kopotun [3], introduced a paper approximation of k -monotone function .
In this paper , we show that if f and g are k -monotone functions on ï›a,bï, such that
       j j f x g x j 1 j 1 
ï¬ ï¬
for all 0 ï‚£ j ï‚£ N , then a direct theorem for the rate of k -monotone
approximation in p L -spaces of the k th usual modulus of smoothness .