On the Rate of Convergence of the Generalized Sz´asz Type Operators for Functions of Bounded VariationU

In this article we introduce the Sz´asz]B´ezier operator Sn, a which is the modified form of the Sz´asz]Mirakyan operator. By means of construction of suitable functions and the methods of Bojanic]Vuillemier w J. Approx. Theory 31 1981., 67]79xand ChengwJ. Approx. Theory 40 1984., 226]241x, using some results and techniques of probability theory, we obtain the rate of convergence of Sn, a for functions of bounded variation. Our results extend and sharpen the results of Cheng w J. Approx. Theory 40 1984., 226]241x, Guo and KhanwJ. Approx. Theory 58 1989., 90]101x for the Sz´asz-Mirakyan operator.