Approximation of a Function Belonging to Lip (ɑ, θ, w) by (C, 1) (E, q)

We discuss whether on not it is possible to have interpolatory estimates in the approximation of a function $f є W^r [0,1]$ by polynomials. The problem of positive approximation is to estimate the pointwise degree of approximation of a function $f є C^r [0,1] \cap \Delta^0$ where $\Delta^0$ is the set of positive functions on [0,1]. Estimates of the form (1) for positive approximation are known ([1],[2]). The problem of monotone approximation is that of estimating the degree of approximation of a monotone nondecreasing function by monotone nondecreasing polynomials. Estimates of the form (1) for monotone approximation were proved in [3],[4],[8]. In [3],[4] is consider $r є , r > 2$. In [8] is consider $r є , r > 2$. It was proved that for monotone approximation estimates of the form (1) are fails for $r є , r > 2$. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is that of estimating the degree of approximation of a convex function by convex polynomials. The problem of convex approximation is consider in ([5],[6]). In [5] is consider $r є , r > 2$. In [6] is consider $r є , r > 2$. It was proved that for convex approximation estimates of the form (1) are fails for $r є , r > 2$. In this paper the question of approximation of function $f є W^r \cap \Delta^1, r є (3,4)$ by algebraic polynomial $p_n є \Pi_n \cap \Delta^1$ is consider. The main result of the work generalize the result of work [8] for $r є (3,4)$.

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Degree of approximation of a function belonging to weighted $(L_r ,\xi(t ))$ class by (C,1)(E,q) means

Tamkang Journal of Mathematics ◽

10.5556/j.tkjm.42.2011.514.31-37 ◽

2011 ◽

Vol 42 (1) ◽

Cited By ~ 2

Author(s):

Hare Krishna Nigam

Keyword(s):

Degree Of Approximation ◽

Approximation Of A Function

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Approximation of a Function Belonging to Lip ((α, r) Class by Np,q. C1 Summability Method of its Fourier Series

Nepal Journal of Science and Technology ◽

10.3126/njst.v14i2.10424 ◽

2014 ◽

Vol 14 (2) ◽

pp. 117-122 ◽

Cited By ~ 4

Author(s):

JP Kushwaha ◽

BP Dhakal

Keyword(s):

Fourier Series ◽

Science And Technology ◽

Degree Of Approximation ◽

Summability Method ◽

Approximation Of A Function

In this paper, an estimate for the degree of approximation of a function belonging to Lip(α, r) class by product summability method Np.q.C1 of its Fourier series has been established. DOI: http://dx.doi.org/10.3126/njst.v14i2.10424 Nepal Journal of Science and Technology Vol. 14, No. 2 (2013) 117-122

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Fractal approximation of a function from a countable sample set and associated fractal operator

Revista de la Real Academia de Ciencias Exactas Físicas y Naturales Serie A Matemáticas ◽

10.1007/s13398-019-00772-8 ◽

2019 ◽

Vol 114 (1) ◽

Cited By ~ 1

Author(s):

P. Viswanathan

Keyword(s):

Fractal Operator ◽

Fractal Approximation ◽

Sample Set ◽

Approximation Of A Function

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On the Joint Approximation of a Function and its Derivatives in the Mean

Ukrainian Mathematical Journal ◽

10.1007/s11253-019-01645-4 ◽

2019 ◽

Vol 71 (2) ◽

pp. 296-307

Author(s):

O. V. Motorna ◽

V. P. Motornyi

Keyword(s):

Joint Approximation ◽

The Mean ◽

Approximation Of A Function

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Approximation of a Function f Belonging to Generalized Hölder Class of Order 0 < α ≤ 1 and Generalized Lipschitz class by Haar Wavelet Method

National Academy Science Letters ◽

10.1007/s40009-019-00835-9 ◽

2019 ◽

Vol 43 (3) ◽

pp. 271-275

Author(s):

Shyam Lal ◽

Vivek Kumar Sharma

Keyword(s):

Haar Wavelet ◽

Lipschitz Class ◽

Wavelet Method ◽

Haar Wavelet Method ◽

Hölder Class ◽

Holder Class ◽

Generalized Lipschitz Class ◽

Approximation Of A Function

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Two variants of Monte Carlo projection method for numerical solution of nonlinear Boltzmann equation

Russian Journal of Numerical Analysis and Mathematical Modelling ◽

10.1515/rnam-2019-0012 ◽

2019 ◽

Vol 34 (3) ◽

pp. 143-150

Author(s):

Sergey V. Rogasinsky

Keyword(s):

Boltzmann Equation ◽

Projection Method ◽

Orthonormal Basis ◽

Statistical Modelling ◽

Hermite Functions ◽

Nonlinear Boltzmann Equation ◽

Kinetic Boltzmann Equation ◽

Relaxation Problem ◽

Nonlinear Kinetic ◽

Approximation Of A Function

Abstract The paper is focused on justification of a statistical modelling algorithm for solution of the nonlinear kinetic Boltzmann equation on the base of a projection method. Hermite functions are used as an orthonormal basis. The error of approximation of a function by a partial sum of Hermite functions series is estimated in the L2 norm. The estimates are compared for two variants of the projection method in the case of solutions to the homogeneous gas relaxation problem with a known solution.

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