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M. Mursaleen

Publications and source records attributed to M. Mursaleen.

24 records · Page 2Linked to original sources
arXiv2015

Approximation by Kantorovich type (p,q)-Bernstein-Schurer Operators

In this paper, we introduce a Shurer type genaralization of (p,q)-Bernstein-Kantorovich operators based on (p,q)-integers and we call it as (p,q)-Bernstein-Schurer Kantorovich operators. We study approximation properties for these operators based on Korovkin's type approximation theorem and also study some direct theorems. Furthermore, we give comparisons and some illustrative graphics for the convergence of operators to some function.

math.CA↗
arXiv2015

Approximation by a Kantorovich type q-Bernstein-Stancu operators

In this paper, we introduce a Kantorovich type generalization of q-Bernstein-Stancu operators. We study the convergence of the introduced operators and also obtain the rate of convergence by these operators in terms of the modulus of continuity. Further, we study local approximation property and Voronovskaja type theorem for the said operators. We show comparisons and some illustrative graphics for the convergence of operators to a certain function.

math.CA↗
arXiv2015

Some approximation properties of bivariate Bleimann-Butzer and Hahn operators based on (p,q)-integers

Recently, Mursaleen et al applied (p,q)-calculus in approximation theory and introduced (p,q)-analogue of Bernstein operators in [16]. In this paper, we construct and introduce a generalization of the bivariate Bleimann-Butzer-Hahn operators based on (p,q)-integers and obtain Korovkin type approximation theorem of these operators. Furthermore, we compute the rate of convergence of the operators by using the modulus of continuity and Lipschitz type maximalfunctions.

math.CA↗
arXiv2015

Stability of Some Positive Linear Operators on Compact Disk

Recently, Popa and Rasa [18,19] have shown the (in)stability of some classical operators defined on [0,1] and found best constant when the positive linear operators are stable in the sense of Hyers-Ulam. In this paper we show Hyers-Ulam (in)stability of complex Bernstein-Schurer operators, complex Kantrovich-Schurer operators and Lorentz operators on compact disk. In the case when the operator is stable in the sense of Hyers and Ulam, we find the infimum of Hyers-Ulam stability constants for respective operators.

math.CA↗
arXiv2015

Approximation by (p,q)-Lorentz polynomials on a compact disk

In this paper, we introduce a new analogue of Lorentz polynomials based on (p,q)-integers and we call it as (p,q)-Lorentz polynomials. We obtain quantitative estimate in the Voronovskaja's type thoerem and exact orders in simultaneous approximation by the complex (p,q)-Lorentz polynomials of degree n, where q > p > 1 attached to analytic functions in compact disks of the complex plane.

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