(p, q)-Generalization of Szasz-Mirakjan operators and their approximation properties

Abstract

We introduce a new modification of (p, q)-analogue of Szasz-Mirakjan operators. Firstly, we give a recurrence relation for the moments of (p, q)-analogue of Szasz-Mirakjan operators and present some explicit formulae for the moments and central moments up to order 4. Next, we obtain quantitative estimates for the convergence in the polynomial weighted spaces. In addition, we give the Voronovskaya theorem for the new (p, q)-Szasz-Mirakjan operators.