Nurhayat Ispir

Approximation by modified Szasz—Mirakjan operators on weighted spaces

The theorems on weighted approximation and the order of approximation of continuous functions by modified Szasz—Mirakjan operators on all positive semi-axis are established.

Rate of convergence of generalized rational type Baskakov operators

We consider the operators introduced in [V. Gupta, N. Ispir, On the Bezier variant of generalized Kantorovich type Balazs operators, Appl. Math. Lett. 18 (9) (2005) 1053-1061] and estimate their rate of convergence for absolutely continuous functions having a derivative coinciding a.e. with a function of bounded variation.

ON SIMULTANEOUS APPROXIMATION FOR SOME MODIFIED BERNSTEIN-TYPE OPERATORS

for n ≥ α, where α, β are integers satisfying α ≥ β ≥ 0 and In ⊆ {0,1,2, . . . ,n} is a certain index set. For α = β = 0, In = {0}, this definition reduces to the BernsteinDurrmeyer operators, which were first studied by Derriennic [3]. Also if α = β = 1, In = {0}, we obtain the recently introduced sequence of Gupta and Maheshwari [4], that is, Mn,1,1(f ,x)≡ Pn(f ,x) which is defined as Pn(f ,x)= ∫ 1

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.

Approximation properties of complex q-Balázs-Szabados operators in compact disks

This paper deals with approximating properties and convergence results of the complex q-Balázs-Szabados operators attached to analytic functions on compact disks. The order of convergence and the Voronovskaja-type theorem with quantitative estimate of these operators and the exact degree of their approximation are given. Our study extends the approximation properties of the complex q-Balázs-Szabados operators from real intervals to compact disks in the complex plane with quantitative estimate.MSC:30E10, 41A25.

q - Bernstein-Schurer-Durrmeyer type operators for functions of one and two variables

The purpose of this paper is to obtain some direct results for the Durrmeyer variant of q - Bernstein-Schurer operators for functions of one variable introduced by Acu et?al. 1. We also propose to study the bivariate extension of these operators and discuss the rate of convergence by using the modulus of continuity, the degree of approximation for the Lipschitz class of functions and the Voronovskaja type asymptotic theorem. Furthermore, we show the convergence of the operators by illustrative graphics in Maple to certain functions in both one and two dimensional cases.

GBS operators of Bernstein-Schurer-Kantorovich type based on q-integers

Agrawal et?al. (2015) constructed a bivariate generalization of a new kind of Kantorovich-type q-Bernstein-Schurer operators and studied a Voronovskaja type theorem and the rate of convergence in terms of the Lipschitz class function and the complete modulus of continuity. The concern of this paper is to obtain the degree of approximation for these bivariate operators in terms of the partial moduli of continuity and the Peetres K-functional. Finally, we construct the GBS (Generalized Boolean Sum) operators of bivariate q-Bernstein-Schurer-Kantorovich type and estimate the rate of convergence for these operators with the help of mixed modulus of smoothness.

On the Bézier variant of generalized Kantorovich type Balazs operators

Abstract In the present work we define the Bezier variant of the generalized Balazs–Kantorovich operators. The special cases of our operators reduce to some well known operators. We establish the rate of convergence for functions of bounded variation for the generalized operators.

Approximation properties of Bezier-summation-integral type operators based on Polya-Bernstein functions

In this article we introduce the Bezier variant of summation integral type operators having Polya and Bernstein basis functions. We give a direct approximation theorem by means of the first order modulus of smoothness and the rate of convergence for absolutely continuous functions having a derivative equivalent to a function of bounded variation.

Rate of convergence of Lupas Kantorovich operators based on Polya distribution

In the present paper, we consider the Kantorovich modification of Lupas operators based on Polya distribution. We estimate the rate of convergence for absolutely continuous functions having a derivative coinciding a.e. with a function of bounded variation.