Approximation Properties of New Lupas-type Operators

In this book, I studied the approximation properties of a sequence of Lupas-type operators Ln (f;x) on the space C[0, ). Then I define the sequence L n (f;x) which represented a generalization of the operators Ln (f;x) on the space C [0, ). I applying the development of Bauer and Donner on Korovkin theorem, and define the m-th order moment T (n,m) (x), also, I proved the Voronoviskaja-type asymptotic formula for the operators L n.Finally, I define the sequence L (n,m) (f;x) on the space C( ,q) ([0, )×[0, )) which represented an extension of the operators L n on two dimensions (x,y) also applying the development of Bauer and Donner on Korovkin theorem, then proved the Voronoviskaja-type asymptotic formula for the operators L (n,m) (f;x,y). All above results lead us to show that the three operators Ln, L n and L _(n,m) have the same order of approximation.

Autorentext

I am Mrs.Haneen J. Sadiq lecturer in mathematics department/college of Science/Basrah university. Born on 20/12/1980.Completed a B.Sc. degree during the period 1998-2002. I got a master degree during the period 2005-2007. My specialization in approximation theory. I have been published several research papers in my specialty on 2014, 2015 and 2016.