Approximation by modified Durrmeyer type Jakimovski-Leviatan operators

Abstract

In the present paper, the modified Durrmeyer type Jakimovski-Leviatan operators are presented and their approximation properties are examined. It has shown that the new operators are the Gamma transform of the Jakimovski-Leviatan operators. The degree of approximation is given by the modulus of continuity. It has been stressed that, there are other operators having the same error estimation with the operators, arising from the Sz & aacute;sz-Durrmeyer operators. Then the degree of global approximation is obtained in a special Lipschitz type function space. Further, a Voronovskaja type asymptotic formula and Gr & uuml;ss-Voronovskaja type theorem are given. The approximation with these operators is visualized with the help of error tables and graphical examples.