Simultaneous Approximation for Generalized Baskakov-Durrmeyer-Type Operators (original) (raw)
On Simultaneous Approximation for Certain Baskakov Durrmeyer Type Operators
Journal of Inequalities in Pure and Applied Mathematics, 2006
In the present paper, we study a certain integral modification of the well known Baskakov operators with the weight function of Beta basis function. We establish pointwise convergence, an asymptotic formula an error estimation and an inverse result in simultaneous approximation for these new operators.
Simultaneous approximation by certain Baskakov–Durrmeyer–Stancu operators
In the present paper, we establish some direct results in simultaneous approximation for Baskakov-Durrmeyer-Stancu (abbr. BDS) operators D ða;bÞ n ðf; xÞ. We establish point-wise convergence, Voronovskaja type asymptotic formula and an error estimate in terms of second order modulus of continuity of the function.
Approximation Of Function By alpha−\alpha-alpha−Baskakov Durrmeyer Type Operators
2020
In the present note, we give the generalization of α−Baskakov Durrmeyer operators depending on a real parameter ρ > 0. We present the approximation results in Korovkin and weighted Korovkin spaces. We also prove the order of approximation, rate of approximation for these operators. In the end, we verify our results with the help of numerical examples by using Mathematica.
Approximation by modified Jain–Baskakov operators
Georgian Mathematical Journal, 2019
In the present paper, we discuss the approximation properties of Jain–Baskakov operators with parameterc. The paper deals with the modified forms of the Baskakov basis functions. Some direct results are established, which include the asymptotic formula, error estimation in terms of the modulus of continuity and weighted approximation. Also, we construct the King modification of these operators, which preserves the test functions{e_{0}}and{e_{1}}. It is shown that these King type operators provide a better approximation order than some Baskakov–Durrmeyer operators for continuous functions defined on some closed intervals.
Simultaneous Approximation of New Sequence of Integral Type Operators with Parameter δ_0
European Journal of Pure and Applied Mathematics, 2019
In this paper, we define a new sequence of linear positive operators of integral type to approximate functions in the space,. First, we study the basic convergence theorem in simultaneous approximation and then study Voronovskaja-type asymptotic formula. Then, we estimate an error occurs by this approximation in the terms of the modulus of continuity. Next, we give numerical examples to approximate three test functions in the space by the sequence. Finally, we compare the results with the classical sequence of Szãsz operators on the interval . It turns out that, the sequence gives better than the results of the sequence for the two test functions using in the numerical examples.
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2018
In the present paper, we introduce Jakimovski-Leviatan-Durrmeyer type operators involving multiple Appell polynomial. First, we investigate Korovkin type approximation theorem and rate of convergence by using usual modulus of continuity and class of Lipschitz function. Next, we study the convergence of these operators in weighted space of functions and estimate the approximation properties. We have also established Voronovskaja type asymptotic formula. Furthermore, we obtain statistical approximation properties of these operators with the help of universal Korovkin type statistical approximation theorem. Some graphical examples for the convergence of our operators towards some functions are given. At the end, we have computed error estimation as our numerical example. Keywords Multiple Apple polynomial • Durrmeyer operators • Jakimovski-Leviatan operators • Modulus of continuity • Statistical approximation Mathematics Subject Classification 41A10 • 41A28 • 41A36
Durrmeyer variant of Apostol-Genocchi-Baskakov operators
Quaestiones Mathematicae, 2020
We study the approximation behavior of the Durrmeyer form of Apostol-Genocchi polynomials with Baskakov type operators including K-functional and second-order modulus of smoothness, Lipschitz space and find the rate of convergence for continuous functions whose derivative satisfies the condition of bounded variation. In the last section, we estimate weighted approximation behavior for these operators.
Convergence of Certain Baskakov Operators of Integral Type
Symmetry, 2021
In the present paper, we propose a Baskakov operator of integral type using a function φ on [0,∞) with the properties: φ(0)=0,φ′>0 on [0,∞) and limx→∞φ(x)=∞. The proposed operators reproduce the function φ and constant functions. For the constructed operator, some approximation properties are studied. Voronovskaja asymptotic type formulas for the proposed operator and its derivative are also considered. In the last section, the interest is focused on weighted approximation properties, and a weighted convergence theorem of Korovkin’s type on unbounded intervals is obtained. The results can be extended on the interval (−∞,0] (the symmetric of the interval [0,∞) from the origin).