Ogün Doğru

Weighted statistical approximation by kantorovich type q-Szász–Mirakjan operators

Abstract In the present paper, we introduce a Kantorovich type modification of q-Szasz–Mirakjan operators and obtain weighted statistical approximation properties of these operators. Also for introduced operators, we give a Voronovskaja type theorem related to q-derivatives.

Statistical approximation properties of q-Bleimann, Butzer and Hahn operators

The main aim of this study is to introduce a new generalization of q-Bleimann, Butzer and Hahn operators and obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function are also established. Our results show that rates of convergence of our operators are at least as fast as classical BBH operators. The second aim of this study is to construct a bivariate generalization of the operator and also obtain the statistical approximation properties.

Bleimann, Butzer, and Hahn operators based on the -integers.

We give a new generalization of Bleimann, Butzer, and Hahn operators, which includes-integers. We investigate uniform approximation of these new operators on some subspace of bounded and continuous functions. In Section, we show that the rates of convergence of the new operators in uniform norm are better than the classical ones. We also obtain a pointwise estimation in a general Lipschitz-type maximal function space. Finally, we define a generalization of these new operators and study the uniform convergence of them.

On statistical approximation properties of Kantorovich type q-Bernstein operators

In this study a new Kantorovich type generalization of q-Bernstein operators is introduced with the help of some recent studies on q-calculus. Then the statistical Korovkin type approximation properties of these operators are investigated. Finally, the order of statistical approximation is examined by means of modulus of continuity and with the help of the elements of Lipschitz class.

q-Szász―Mirakyan―Kantorovich type operators preserving some test functions

Abstract In this paper, we introduce a q -analogue of the Szasz–Mirakyan–Kantorovich operators and we propose two different modifications of the q -Szasz–Mirakyan–Kantorovich operators. These modifications preserve some test functions. We also examine the rate of convergence for the constructed operators by means of modulus of continuity.

ON STATISTICAL APPROXIMATION PROPERTIES OF THE KANTOROVICH TYPE LUPAS OPERATORS

Abstract In this study, a Kantorovich type generalization of Lupas operators is introduced. Then the Korovkin type statistical approximation properties of these operators are investigated. Finally, the rates of statistical convergence of this modification are also studied.

Statistical approximation by a modification of q-Meyer-König and Zeller operators

Abstract In this work, we introduce a modification of the q -Meyer-Konig and Zeller operators, and investigate the Korovkin type statistical approximation properties of this modification via A -statistical convergence. Also we prove that this modification provides a better estimation than the q -MKZ operators on the interval [ α n , 1 ) ⊂ [ 1 2 , 1 ) by means of the modulus of continuity.

On Kantorovich Process of a Sequence of the Generalized Linear Positive Operators

We define the Kantorovich variant of the generalized linear positive operators introduced by Ibragimov and Gadjiev in 1970. We investigate direct approximation result for these operators on p-weighted integrable function spaces and also estimate their rate of convergence for absolutely continuous functions having a derivative coinciding a.e., with a function of bounded variation.

King type modification of Meyer-König and Zeller operators based on the q-integers

In the present paper, introducing a King type modification of the Meyer-Konig and Zeller (MKZ) operators, we prove that the error estimation of these operators is better than the classical MKZ operators. Furthermore, a King type modification of the q-MKZ is also introduced and the rate of convergence of this modification is examined.

Statistical approximation by Stancu type bivariate generalization of Meyer-König and Zeller type operators

The main aim of this study is to introduce a new generalization of Meyer-Konig and Zeller type operators in order to improve the rate of statistical convergence. The second purpose of this study is to introduce a Stancu type bivariate generalization of the operator defined in this note. Using statistical convergence, we will also give the statistical approximation properties and Popoviciu type rate of convergence of these operators.