Improved rate of approximation by modification of Baskakov operator
Animesh Gairola, Amrita Singh, Laxmi Rathour, Vishnu Narayan Mishra · Operators and Matrices · 2022
The optimal order of approximation, |L n f (x)f (x)| of a linear positive operator L n f (x) is 1/n and can not be improved however smooth the function may be. We remove the positivity of the Baskakov operator V n ( f ;x) and introduce its three variants V M,i n ( f ;x) , i = 1,2,3. We prove that the rates of approximation by these operators are improved from the linear order 1/n to quadratic order 1/n 2 and then to cubic order 1/n 3 for sufficiently smooth functions.