Abstract
In this article, we define and study a family of modified Baskakov type operators based on a parameter . This family is a generalization of the classical Baskakov sequence. First, we prove that it converges to the function being approximated. Then, we find a Voronovsky-type formula and obtain that the order of approximation of this family is . This order is better than the order of the classical Baskakov sequence whenever . Finally, we apply our sequence to approximate two test functions and analyze the numerical results obtained.
Highlights
The well-known classical Baskakov sequence is defined as [1] ( ) ∑ () ./ ( ) where () ( ) ( ), )Many modifications to the above sequence were applied by several researchers, all reaching the same order of approximation ( ) [2, 3, 4]
We give some theorems in simultaneous approximation for the sequence ( )
We describe the results by the graphics of each test function and its three approximations for each value of
Summary
Many modifications to the above sequence were applied by several researchers, all reaching the same order of approximation ( ) [2, 3, 4]. There are some techniques, such as the linear combination and Micchelli combination, that were defined and studied for many sequences of positive and linear operators to modify the approximation order by these sequences. Pallini [9] presented a modification of the sequence of classical Bernstein polynomials with a different order of approximation. His sequence depends on a parameter and is defined as follows ( )∑(.
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