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  Volume 7, Issue 1, Article 23
On a Hybrid Family of Summation Integral Type Operators

    Authors: Vijay Gupta, Esra Erkus,  
    Keywords: Linear positive operators, Summation-integral type operators, Rate of convergence, Asymptotic formula, Error estimate, Local direct results, $K$-functional, Modulus of smoothness, Simultaneous approximation.  
    Date Received: 21/11/05  
    Date Accepted: 01/12/05  
    Subject Codes:

41A25; 41A30.

    Editors: Alexandru Lupas (1942-2007),  

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.

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