On q-Parametric Szász-Mirakjan Operators

Abstract

In the present paper, we introduce q-parametric Szász-Mirakjan operators. We study convergence properties of these operators Sn,q(f ). We obtain inequalities for the weighted approximation error of q-Szász-Mirakjan operators. Such inequalities are valid for functions of polynomial growth and are expressed in terms of weighted moduli of continuity. We also discuss Voronovskaja-type formula for q-Szász-Mirakjan operators.Mathematics Subject Classification (2010). Primary 41A35; Secondary 39A13.

Stancu type (p; q)-Szász-Mirakyan-Baskakov operators

“…The operators (1.2) are linear and positive and for p = 1; the operators (1.2) turn out to be q-Szász-Mirakyan operators de…ned in [14]. King type modi…cation of (p; q)-Szász-Mirakyan operators was introduced in [2].…”

STANCU TYPE GENERALIZATION OF MODIFIED GAMMA OPERATORS BASED ON q-INTEGERS

“…Phillips [15] first introduced the q-analogue of well-known Bernstein polynomials. After that, many other authors introduced modifications of the other important operators based on the q-integers, for example, q-Meyer-König operators [18], q-Bleimann, Butzer and Hahn operators [14], q-Szász-Mirakyan operators [13], q-Baskakov operators [5] and so on [6], [8], [9]. Now we mention certain definitions based on q-integers and the details can be found in [10].…”

Weighted approximation properties of Stancu type modification of q-Szász-Durrmeyer operators

“…Based on q-exponential function Mahmudov [21], introduced the following q-Szász-Mirakyan operators S n;q (f;…”