Approximation by modified Jain–Baskakov operators.

In the present paper, we discuss the approximation properties of Jain–Baskakov operators with parameter c. The paper deals with the modified forms of the Baskakov basis functions. Some direct results are established, which include the asymptotic formula, error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct the King modification of these operators, which preserves the test functions e 0 {e_{0}} and e 1 {e_{1}}. It is shown that these King type operators provide a better approximation order than some Baskakov–Durrmeyer operators for continuous functions defined on some closed intervals. [ABSTRACT FROM AUTHOR]