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

Abstract

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

Approximation Properties of p , q -Szász-Mirakjan-Durrmeyer Operators

“…In [9], Mursaleen et al proposed two different Kantorovich-type ðp, qÞ-Szász-Mirakjan operators and discussed their error estimated. In [10], Kara and Mahmudov constructed a new ðp, qÞ-Szász-Mirakjan operators as Definition 1. Let 0 < q < p ≤ 1 and m ∈ ℕ.…”

On Stancu-Type Generalization of Modified p , q -Szász-Mirakjan-Kantorovich Operators

“…In [12], Acar first proposed ðp, qÞ-Szász-Mirakjan operators defined on ½0, ∞Þ. In [13], Kara et al constructed a modified ðp, qÞ-Szász-Mirakjan as follows:…”