Direct estimates of certain Mihesan-Durrmeyer type operators

Document Type: Original Article


Central University of Haryana, India


In this note we consider a Durrmeyer type operator having the basis functions in summation and integration due to Mihe\c{s}an [Creative Math. Inf. 17 (2008), 466--472.] and P\v{a}lt\v{a}nea [Carpathian J. Math. 24 (2008), no. 3, 378--385.] that preserve the linear functions. We present a Voronovskaja type theorem, local approximation theorem by means of second order modulus of continuity and weighted approximation for these operators. In the last section of the paper, we obtain the rate of approximation for absolutely continuous functions having a derivative equivalent with a function of bounded variation.