Some approximation theorems VIA Statistical convergence

In the note, we obtain the estimates for the rate of convergence for a sequence of q-Bernstein polynomials {Bn,q(f)} for 0 0, α ≠ 1, and the orders do not depend on α, unlike the classical case.

The rate of convergence of q-bernstein polynomials for 0 strict inequality q strict inequality 1

This chapter includes proofs of the existence and uniqueness of the solutions of first order systems of q-difference equations in a neighborhood of a point a, \(a \geq 0\). Then, as applications of the main results, we study linear q-difference equations as well as the q-type Wronskian. These results are mainly based on (Mansour, q-Difference Equations, Master’s thesis, Faculty of Science, Cairo University, Giza, Egypt, 2001). This chapter also includes a section on the asymptotics of zeros of some q-functions.

q -Difference Equations

In the present paper, we introduce q-parametric Szasz-Mirakjan operators. We study convergence properties of these operators S
 n,q(f). We obtain inequalities for the weighted approximation error of q-Szasz-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-Szasz-Mirakjan operators.

On q-Parametric Szász-Mirakjan Operators

In the present paper we introduce and investigate weighted statistical approximation properties of a q-analogue of the Baskakov and Baskakov-Kantorovich operators. By using a weighted modulus of smoothness, we give some direct estimations for error in the case 0 < q < 1.

Statistical approximation of Baskakov and Baskakov-Kantorovich operators based on the q-integers

In the present paper we introduce a q-analogue of the Bernstein-Kantorovich operators and investigate their approximation properties. We study local and global approximation properties and Voronovskaja type theorem for the q-Bernstein-Kantorovich operators in case 0 < q < 1.

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Approximation Theorems for q-Bernstein-Kantorovich Operators

We introduce a new -parametric generalization of Bleimann, Butzer, and Hahn operators in . We study some properties of -BBH operators and establish the rate of convergence for -BBH operators. We discuss Voronovskaja-type theorem and saturation of convergence for -BBH operators for arbitrary fixed . We give explicit formulas of Voronovskaja-type for the -BBH operators for . Also, we study convergence of the derivative of -BBH operators.

/pdf/parametric-bleimann-butzer-and-hahn-operators-36b748t602.pdf

Parametric Bleimann Butzer and Hahn Operators

In the present paper, we introduce genuine q-Bernstein-Durrmeyer operators and
estimate the rate of convergence for continuous functions in terms of modulus of
continuity. Furthermore we study some direct results for the genuine q-Bernstein-Durrmeyer operators.

On genuine q-Bernstein--Durrmeyer operators

In this paper, we estimate the third and the fourth order central moments for the difference of the Lupas q-analogue of the Bernstein operator and the limit q-Lupas operator. We also prove a quantitative variant of Voronovskaja's theorem for Rn;q. AMS subject classications : 65D10, 92C45

/pdf/voronovskaja-type-theorem-for-the-lupas-q-analogue-of-the-2t4z0xxmfy.pdf

Voronovskaja type theorem for the Lupaş q-analogue of the Bernstein operators

In this paper, we define a new Kantorovich type q-analogue of the Balazs–Szabados operators, we give some local approximation properties of these operators and prove a Voronovskaja type theorem.

/pdf/some-approximation-properties-of-new-kantorovich-type-q-3z98e8tt0g.pdf

Pembe Sabancigil

Papers

Approximation Theorems for q-Bernstein-Kantorovich Operators

Parametric Bleimann Butzer and Hahn Operators

On genuine q-Bernstein--Durrmeyer operators

Voronovskaja type theorem for the Lupaş q-analogue of the Bernstein operators

Some approximation properties of new Kantorovich type q -analogue of Balázs–Szabados operators