Study of sensitivity of parameters of Bernstein-Stancu operators
نویسندگان
چکیده
This paper is aimed at studying sensitivity of parameters α and β appearing in the operators introduced by D.D. Stancu [11] in 1969. Results are established on the behavior the nodes used in Bernstein-Stancu polynomials and the nodes used in Bernstein polynomials and graphical presentations of them are generated. Alternate proof of uniform convergence of Bernstein-Stancu operators and an upper bound estimation are derived. It is also established that the parameters α and β in Bernstein-Stancu polynomials can be used to get better approximation at a point x = α/β in [0, 1] to the Bernstein polynomials.
منابع مشابه
Approximation by $(p,q)$-Lupac{s} Stancu Operators
In this paper, $(p,q)$-Lupas Bernstein Stancu operators are constructed. Statistical as well as other approximation properties of $(p,q)$-Lupac{s} Stancu operators are studied. Rate of statistical convergence by means of modulus of continuity and Lipschitz type maximal functions has been investigated.
متن کاملBlending Type Approximation by Bernstein-durrmeyer Type Operators
In this note, we introduce the Durrmeyer variant of Stancu operators that preserve the constant functions depending on non-negative parameters. We give a global approximation theorem in terms of the Ditzian-Totik modulus of smoothness, a Voronovskaja type theorem and a local approximation theorem by means of second order modulus of continuity. Also, we obtain the rate of approximation for absol...
متن کاملOn q-analogue of Bernstein-Schurer-Stancu operators
Keywords: q-Bernstein–Schurer–Stancu operators q-integers Modulus of smoothness Rate of convergence a b s t r a c t In the present paper, we introduce the Stancu type generalization of the Bernstein–Schurer operators based on q integers. First, we prove the basic convergence of S ða;bÞ n;p ð:; q; xÞ and then obtain the rate of convergence by these operators in terms of the modulus of continuity...
متن کاملPointwise approximation by a Durrmeyer variant of Bernstein-Stancu operators
In the present paper, we introduce a kind of Durrmeyer variant of Bernstein-Stancu operators, and we obtain the direct and converse results of approximation by the operators.
متن کاملSome statistical approximation properties of Kantorovich-type q-Bernstein-Stancu operators
In this paper two kinds of Kantorovich-type q-Bernstein-Stancu operators are introduced, and the statistical approximation properties of these operators are investigated. Furthermore, by means of modulus of continuity, the rates of statistical convergence of these operators are also studied. MSC: 41A10; 41A25; 41A36
متن کامل