Mediha Örkcü

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.

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.

Approximation properties of bivariate extension of q-Szász-Mirakjan-Kantorovich operators

In the present paper, a bivariate generalization of the q-Szász-Mirakjan-Kantorovich operators is constructed by qR-integral and these operators’ weighted A-statistical approximation properties are established. Also, we estimate the rate of pointwise convergence of the proposed operators by modulus of continuity.MSC:41A25, 41A36.

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.

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.

Some approximation properties of the generalized Baskakov operators

Abstract The present paper deals with a generalization of the Baskakov operators. Some direct theorems, asymptotic formula and A-statistical convergence are established. Our results are based on a ρ function. These results include the preservation properties of the classical Baskakov operators.

Approximation properties of modified Szász–Mirakyan operators in polynomial weighted space

We introduce certain modified Szász–Mirakyan operators in polynomial weighted spaces of functions of one variable. We studied approximation properties of these operators.