商品簡介
In this book, firstly we study four sequences of linear positive operators (L ̃_n )_λ (f;x),λ=1,2,3,4 to approximate functions belongs to the space of exponential growth. We introduce some direct results for these operators and then we show that the operators (L ̃_n )_λ ((p) ) (f;x) converge to the function f ((p) ) (x) where p=0,1,2,3 and n→∞. Next, we prove the Voronovskaja-type asymptotic formulas for these operators.Secondly, we introduce a generalization for each sequence of operators (L ̃_n )_λ (f;x) denoted by (M_n )_λ (f;x) respectively, where λ=1,2,3,4. We show that the operators (M_n )_λ ((p) ) (f;x) converge to the function f ((p) ) (x) where p=0,1,2,3 and n→∞. Also we estimate that the Voronovskaja-type asymptotic formulas for these operators. Finally, we introduce two modifications (S_n )_λ (f;x),λ=1,2 of summation-integral type operators to approximate bounded integrable functions on the interval 0,∞). Then we prove that the operators (S_n )_λ ((p) ) (f;x) are approximation for f ((p) ) (x) as n→∞ where p=0,1,2,3. Also, we prove the Voronovskaja-type asymptotic for these operators.
