( p , q ) $(p,q)$ -Generalization of Szász–Mirakjan operators and their approximation properties

Abstract

Abstract We introduce a new modification of ( p , q ) $(p,q)$ -analogue of Szász–Mirakjan operators. Firstly, we give a recurrence relation for the moments of ( p , q ) $(p,q)$ -analogue of Szász–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 ) $(p,q)$ -Szász–Mirakjan operators.

Keywords

• ( p , q ) $(p,q)$ -Integers
• ( p , q ) $(p,q)$ -Szász–Mirakjan operators
• Weighted approximation