Stancu type generalization of q-Favard–Szàsz operators

Abstract

Abstract. In this paper, we introduce a Stancu type generalization of the q−Favard-Szàsz operators, estimate the rates of statistical convergence and study the local approximation properties of these operators.

Some approximation properties of Kantorovich variant of Chlodowsky operators based on q-integer

“…K 5 = q 6 + 3q 5 + 6q 4 + 10q 3 + 9q 2 + 7q + 4 [5] q ; K 6 = q 6 + 4q 5 + 11q 4 + 18q 3 + 15q 2 + 11q + 5 [5] q ;…”

“…They investigated the rate of convergence and the monotonicity property of these operators. For more works, see references [4,5,6,7,8,9,10]. In this study, we de…ne Kantorovich type generalization of q Chlodowsky operators.…”

Approximation by Chlodowsky type q-Jakimovski-Leviatan operators

“…The authors proved approximation theorems and the rate of convergence theorems for these operators. Later in [9] a Stancu type generalization of the above q-Favard-Szasz operators are de…ned as…”

“…The approximation properties and rates of convergence results for these operators are obtained in the statistical sense. Very recently, A. Karaisa [10] de…ned Chlodowsky type generalization of the q-Favard-Szasz operators as follows:…”

Approximation by Durrmeyer type Jakimoski–Leviatan operators

“…Later, Büyükyazıcı et al [3] have defined the Chodowsky type generalization of the Favard-Szàsz operators by means of Appell polynomials. In addition, we refer to the following studies related to the approximation properties of some operators [4][5][6][7][8][9][10][11][12]. For the sake shortness, we denote the notation F n D Q n iD0 .n i/ throughout the paper.…”