Bernstein polynomial

Applied mathematics

Convergence (economics)

Constant coefficients

Economics

Computer science

Limit (mathematics)

Bounded function

Computer network

Baskakov operator

Microlocal analysis

Fourier integral operator

Mathematics

Rate of convergence

Mathematical analysis

Approximation theory

Programming language

Economic growth

Channel (broadcasting)

Linear operators

Operator theory

Constant (computer programming)

Iranian Journal of Science and Technology Transactions A Science

Approximation theory has a significant place in the studies in mathematics, and the researches on it are increasing with each passing day. Accordingly, a number of studies have been presented about Bernstein approximation which is one of the most known linear positive operators. In this study, a new modification of Bernstein operators which fix constant and preserve Korovkin’s other test functions in limit case has been introduced. Then, the approximation properties of the newly defined operators such as asymptotic formulas, weighted approximation and rate of convergence have been presented. Moreover, numerical simulations are included. Finally, discussion and conclusions are presented.

On New Modification of Bernstein Operators: Theory and Applications