Generalized Szász-Mirakjan Operator Approximation

In this paper we shall defin a kind of generahzed Szász-Mirakjan operator and discussits convergence and degree of approximation,extend some results got by J.Grof and Z.Ditzian.     

The Approximation of Continuous Functions by Jackson Operator

Let f(x): R~＇→R~＇be a continuous function with period 2π,i. e, f(x)∈C_2~·D. Jackson singular integral operator of f(x) is defined by: According to [1], for any f(x)∈C_2x, Then     

Approximation by modified Szász-Durrmeyer operators

The main goal of this paper is to introduce Durrmeyer modifications for the generalized Szász–Mirakyan operators defined in (Aral et al., in Results Math 65:441–452, 2014). The construction of the new operators is based on a function \(\rho \) which is continuously differentiable \(\infty \) times on \( \left[ 0,\infty \right) ,\) such that \(\rho \left( 0\right) =0\) and \( \inf _{x\in \left[ 0,\infty \right) }\rho ^{\prime }\left( x\right) \ge 1.\) Involving the weighted modulus of continuity constructed using the function \( \rho \), approximation properties of the operators are explored: uniform convergence over unbounded intervals is established and a quantitative Voronovskaya theorem is given. Moreover, we obtain direct approximation properties of the operators in terms of the moduli of smoothness. Our results show that the new operators are sensitive to the rate of convergence to f,  depending on the selection of \(\rho .\) For the particular case \(\rho \left( x\right) =x\), the previous results for classical Szász-Durrmeyer operators are captured.     

Approximation by the Complex form of a Link Operator Between the Phillips and the Szász–Mirakjan Operators

Results in Mathematics - The link operator $${P_{\alpha}^\rho(f,x)=\sum_{k=1}^\infty s_{\alpha,k}(x)\int_0^\infty \theta_{\alpha,k}^\rho(t)f(t)dt+e^{-\alpha x}f(0)}$$ , $${\alpha, \rho >...     

On the Approximation of Continuous Functions by Pal-Type Interpolation Polynomials

Let us denote by -1=x_n相似文献   

The Approximation of Continuous Function by Kantorovitch Operator and Its Transformation Operator

Kantorovitch polynomials operator is the following extension of Bernstein polynomialsoperatorTransformation operator or K_u[f(t):x]is defined byAccording to [2],for any f(x)∈C_[0,l] then     

On the Approximation of Functions of the Hölder Class by Triharmonic Poisson Integrals

We determine the exact value of the upper bound for the deviation of the triharmonic Poisson integral from functions of the Hölder class.     

On the Approximation of Functions of the Hölder Class by Biharmonic Poisson Integrals

We determine the exact value of the upper bound of the deviation of biharmonic Poisson integrals from functions of the Hölder class.     

Approximation of Multivariate Functions with a Certain Mixed Smoothness by Entire Functions

ＡｐｐｒｏｘｉｍａｔｉｏｎｏｆＭｕｌｔｉｖａｒｉａｔｅＦｕｎｃｔｉｏｎｓｗｉｔｈ　ａＣｅｒｔａｉｎＭｉｘｅｄＳｍｏｏｔｈｎｅｓｓｂｙＥｎｔｉｒｅＦｕｎｃｔｉｏｎｓＷａｎｇＨｅｐｉｎｇ（汪和平）；ＳｕｎＹｏｎｇｓｈｅｎｇ（孙永生）（Ｄｅｐａｒｔｍｅｎｔ...     

Approximation by the Bernstein–Durrmeyer Operator on a Simplex

For the Jacobi-type Bernstein–Durrmeyer operator M _n,κ on the simplex T ^d of ℝ ^d , we proved that for f∈L ^p (W _κ ;T ^d ) with 1<p<∞,

Pointwise Approximation by Szàsz-Mirakjan Quasi-Interpolants

Recently some classical operator quasi-interpolants were introduced to obtain much faster convergence. A.T. Diallo investigated some approximation properties of Szàsz-Mirakjan Quasi-Interpolants, but he obtained only direct theorem with Ditzian-Totik modulus ω2rψ(f, t). In this paper, we extend Diallo's result and solve completely the characterization on the rate of approximation by the method of quasi-interpolants to functions f ∈ CB[0, ∞) by making use of the unified modulus ω2rψλ> (f, t) (0 ≤λ≤ 1).     

Approximation properties of Szász–Mirakyan operators preserving exponential functions

Positivity - This paper is a natural continuation of Acar et al. (Mediterr J Math 14:6, 2017, https://doi.org/10.1007/s00009-016-0804-7 ) where Szász–Mirakyan operators preserving...     

A Characterization of Pointwise Approximation for Linear Combinations of Szász-type Operators

In this paper, we use Ditzian-Totik modulus to study the pointwise approximation for the linear combinations of Szasz-type operators, and obtain the direct and converse theorem and the characterization of the pointwise approximation for the linear combinations of Szasz-type operators.     

On Derivation Approximation of Bernstein Operator

If/is a function defined on【0,1】,then the Bernstein polynomial Bn(,;z)of/is asfollows . 蹦加)==k壹=O蝶‰㈤A㈤:=(:)靠l-x),卜七. (1) If厂is bounded on【0,l】,z is a point if discontinuty of the frist kind,tIerzog and Hill[’Jproved 1 1 撬Bn(加)=主(,(z+)十m一))· (2) Furthermore,Cheng[。】gave the rate of convergence above when,is bounded variationon【0,1】.A question we are interested in is that if,’∈BV[O,l】,what is B,n approximateto l’ll What is error estimation we have obtained? Th…     

On Approximation of Functions by Generalized Abel–Poisson Operators

We find the exact constant in the principal term of the deviation of a function in the Zygmund class from the generalized Abel-Poisson operators determined by the Fourier series over the trigonometric system with particular summation factors.     

Fekete-Szeg? Problem for a Subclass of Meromorphic Functions Defined by the Dziok-Srivastava Operator

By using the hypergeometric function defined by the Dziok-Srivastava operator, a new subclass of meromorphic function is introdued. We obtain Fekete-Szeg? inequalities for the meromorphic function f(z) for which α-(1 + α{1 +z[_lI_mf(z)]′′/[_lI_mf(z)]′}/z[_lI_mf(z)]′/_lI_mf(z))? φ(z)(α∈ C-{1/2, 1}).     

Approximation of a Continuous Curve by its Bernstein-B��zier Operator

In this paper we consider integer and rational parametric Bézier curves and study the distance between the curve and its control polygon. To measure the distance we use first and second order moduli of smoothness of vector-valued function. We consider also NURBS curves with equidistant knots. Some direct approximation theorems will be presented.     

Direct estimates of the weighted simultaneous approximation by the Szász–Mirakjan operator

Periodica Mathematica Hungarica - We establish direct estimates of the rate of weighted simultaneous approximation by the Szász–Mirakjan operator for smooth functions in the supremum...