Tusi Mathematical Research Group (TMRG)Advances in Operator Theory2538-225X2220170401Direct estimates of certain Mihesan-Durrmeyer type operators1621784378510.22034/aot.1612-1079ENArun KajlaCentral University of Haryana, IndiaJournal Article20161212In this note we consider a Durrmeyer type operator having the basis functions in summation and integration due to Mihec{s}an [Creative Math. Inf. 17 (2008), 466--472.] and Pv{a}ltv{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.http://www.aot-math.org/article_43785_96f1e2166cea1812c168d235131ebc57.pdf