Order improvement for the sequence of $\alpha$-Bernstein-Paltanea operators

In the present paper, we give the modifications of $\alpha-$Bernstein-Paltanea operators with better approximation properties. We present three modifications of these operators having linear, quadratic and cubic order of approximation whereas the classical operators are of linear order. By increasing the order of approximation of these operators, the speed of the convergence will be increased. We establish some approximation results concerning the rate of convergence, error estimation and Voronovskaja type formulas for the new modifications. Also, we verify our analytical results with the help of MAPLE algorithms.