Approximation Properties of New Lupas-type Operators.

      Аннотация: In this book, I studied the approximation properties of a sequence of Lupas-type operators L_n (f;x) on the space C[0,?). Then I define the sequence L ?_n (f;x) which represented a generalization of the operators L_n (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 L_n, L ?_n and L ?_(n,m) have the same order of approximation.

Ключевые слова: linear positive operators, Korovkin theorem, Voronoviskaja theorem, Lupas operators