On approximation properties of a new construction of Baskakov operators

Abstract The purpose of this research is to construct sequences Baskakov operators such that their construction consists a function σ by use two sequences, $\xi _{n} $ ξn and $\eta xmlns:mml="http://www.w3.org/1998/Math/MathML">ηn . In these operators, not only features the but also Korovkin set $\lbrace 1,\sigma ,\sigma ^{2} \rbrace xmlns:mml="http://www.w3.org/1998/Math/MathML">{1,σ,σ2} in weighted space fix exactly functions from set. Thereafter, uniform approximation on an unbounded interval, degree with regards modulus continuity, asymptotic formula new are presented. Finally, some illustrative results provided order observe properties newly defined operators. demonstrate introduced provide better terms rate convergence according selection