On approximation properties of a new construction of Baskakov operators

Abstract

Abstract The purpose of this research is to construct sequences of Baskakov operators such that their construction consists of a function σ by use of two function sequences, ξ n $\xi _{n} $ and η n $\eta _{n} $ . In these operators, σ not only features the sequences of operators but also features the Korovkin function set { 1 , σ , σ 2 } $\lbrace 1,\sigma ,\sigma ^{2} \rbrace $ in a weighted function space such that the operators fix exactly two functions from the set. Thereafter, weighted uniform approximation on an unbounded interval, the degree of approximation with regards to a weighted modulus of continuity, and an asymptotic formula of the new operators are presented. Finally, some illustrative results are provided in order to observe the approximation properties of the newly defined Baskakov operators. The results demonstrate that the introduced operators provide better results in terms of the rate of convergence according to the selection of σ.

Keywords

• Baskakov operators
• Rate of convergence
• Voronovskaya type theorem
• Weighted approximation
• Numerical experiments