On a hybrid family of summation integral type operators

The present paper deals with the study of the mixed summation integral type operators having Szász and Baskakov basis functions in summation and integration respectively. Here we obtain the rate of point wise convergence, a Voronovskaja type asymptotic formula, an error estimate in simultaneous approximation. We also study some local direct results in terms of modulus of smoothness and modulus of continuity in ordinary and simultaneous approximation. © 2006 Victoria University. All rights reserved.