Approximation Properties of New Lupas-type Operators
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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) a...
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.
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