On the rate of convergence of two Bernstein-Bezier type operators for bounded variation functions, II

The rates of convergence of two Bernstein-Bezier type operators B-n((alpha) ) and L-n((alpha)) for functions of bounded variation have been studied for the case alpha greater than or equal to 1 by the author and A. Piriou (199 8. J. Approx. Theory 95, 369-387). In this paper the other ease 0 < alpha < 1 is treated and asymptotically optimal estimations of B-n((alpha)) and L- n((alpha)) for functions of bounded variation are obtained. Besides. some i nteresting behaviors of the operators B-n((alpha)) and L-n((alpha)) for mon otone functions and functions of bounded variation are also given. (C) 2000 Academic Press.