Asian Journal of Mathematics and Computer Research

THE APPROXIMATION THEOREMS OF A KIND OF KING-KANTOROVICH-TYPE OPERATORS

GE YANG

College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, P.R. China.

QIULAN QI *

College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050024, P.R. China.

*Author to whom correspondence should be addressed.

---

Abstract

We give a kind of modification of Baskakov and Szász operators, which preserved the test functions 1 and x². Using the unified modulus of continuity and Peetre’s K-functional, we present the direct and converse estimate of these modified operators. Furthermore, the relation of our modified operators and the smoothness property of the functions is also given.

Keywords: Kantorovich operators, modulus of continuity;, Peetre’s K-functional, the H¨older inequality

---

---