Local approximation properties of certain class of linear positive operators via \(I\)-convergence (Q931588)

The authors introduce a certain family of positive linear operators via \(I\)-convergence and gave the direct approximation theorem by the first and the second modulus of continuities. The authors give an example, modified Szasz-Mirakjan operators \[ S_n^{\ast}(f,x)=e^{-na_nx}\sum_{k=0}^{\infty}f(\frac kn)\frac{(na_nx)^k}{k!}, \] where \(I-\lim_{n\rightarrow\infty}a_n=1\) and \(I-\lim_{n\rightarrow\infty}\frac{a_n}{n}=0\) to show that the classical Korovkin Theory does not work but the theory works in \(I\)-convergence sense.