Approximation theorem for new modification of \(q\)-Bernstein operators on (0,1) (Q1983350)

The authors extend the works of Usta and construct modified \(q\)-Bernstein operators using the second central moment of the \(q\)-Bernstein operators defined by Phillips. They study a Korovkin-type approximation theorem, a Voronovskaja type asymptotic formula, local approximation theorems using Peetre's K-functional and the Steklov mean and the rate of convergence. Numerical examples are also illustrated involving graphical representations.