Approximation Properties of Jain-Stancu Operators

Abstract

In the present paper, we introduce the Stancu type Jain operators, which generalize the well-known Szasz-Mirakyan operators via Lagrange expansion. We investigate their weighted approximation properties and compute the error of approximation by using the modulus of continuity. We also give an asymptotic expansion of Voronovskaya type. Finally, we introduce a modified form of our operators, which preserves linear functions, provides a better error estimation than the Jain operators and allows us to give global results in a certain subclass of C[0, infinity). Note that the usual Jain operators do not preserve linear functions and the global results in a certain subspace of C[0, infinity) can not be given for them.