Approximation Of Certain Classes Research Articles

On On the approximation of functions by Jacobi – Dunkl expansion in the weighted space 𝕃 2 ( α , β )

UDC 517.5 We prove some new estimates useful in applications for the approximation of certain classes of functions characterized by the generalized continuity modulus from the space 𝕃 2 ( α , β ) by partial sums of the Jacobi – Dunkl series. For this purpose, we use the generalized Jacobi – Dunkl translation operator obtained by Vinogradov in the monograph [Theory of approximation of functions of real variable, Fizmatgiz, Moscow (1960) (in Russian)].

Upper Bounds for the Approximation of Certain Classes of Functions of a Complex Variable by Fourier Series in the Space L2 and n-Widths

We consider the problem of the mean-square approximation of complex functions regular in a domain D ⊂ C by Fourier serieswith respect to an orthogonal (inD) systemof functions {ϕk(z)}, k = 0, 1, 2,.... For the case inwhich D = {z ∈ C: |z| < 1}, we obtain sharp estimates for the rate of convergence of the Fourier series in the orthogonal system {z k }, k = 0, 1, 2,..., for classes of functions defined by a special mth-order modulus of continuity. Exact values of the series of n-widths for these classes of functions are calculated.

Upper Bounds for the Approximation of Certain Classes of Functions of a Complex Variable by Fourier Series in the Space $L_2$ and $n$-Widths

В работе рассматривается задача среднеквадратичного приближения функций комплексного переменного, регулярных в области $\mathscr D\subset\mathbb C$, рядами Фурье по ортогональной в $\mathscr D$ системе функций $\{\varphi_k(z)\}$, $k=0,1,2,…$ . В случае, когда $\mathscr D=z\in\mathbb C:|z|&lt;1\}$, получены точные оценки скорости сходимости рядов Фурье по ортогональной системе $z^k\}$, $k=0,1,2,…$, на классах функций, задаваемых специальным модулем непрерывности $m$-го порядка. Вычислены точные значения ряда $n$-поперечников на указанных классах функций. Библиография: 17 названий.

Approximation of Certain Classes of Singular Integrals by Algebraic Polynomials

We study the problem of pointwise approximation by algebraic polynomials for classes of functions that are singular integrals of bounded functions. We obtain asymptotically exact estimates of approximations.

On asymptotically exact estimates for the approximation of certain classes of functions by algebraic polynomials

We present a survey of results obtained for the last decade in the field of approximation of specific functions and classes of functions by algebraic polynomials in the spaces C and L 1 and approximation with regard for the location of a point on an interval.

Approximation of certain classes of differentiable functions by generalized splines

We find the exnet value of the best (α, β)-approximation by generalized Chebyshev splines for a class of functions differentiable with weight on [−1, 1].

Approximation of certain classes of smooth periodic functions of several variables by means of interpolation splines defined over a uniform net

Approximation of certain classes of smooth periodic functions of several variables by means of interpolation splines defined over a uniform net

Best approximation of certain classes of smooth functions on the real axis by splines of a higher order

Best approximation of certain classes of smooth functions on the real axis by splines of a higher order

Best one-sided approximation of certain classes of functions

Best one-sided approximation of certain classes of functions

Approximation of certain classes of periodic functions with many variables

Approximation of certain classes of periodic functions with many variables

Approximation of certain classes of periodic functions of two variables by linear methods of summation of their Fourier series

Approximation of certain classes of periodic functions of two variables by linear methods of summation of their Fourier series

Approximation of certain classes of differentiable periodic functions by interpolational splines in a uniform decomposition

In this paper we obtain upper and lower bounds of a uniform approximation by interpolational splines of order r in a uniform decomposition on the classes of functions WrHω and W L r+2 and on the whole space Cr.

The approximation of certain classes of differentiable periodic functions of two variables by Fourier sums

The approximation of certain classes of differentiable periodic functions of two variables by Fourier sums

Best one-sided approximation of certain classes of functions

This considers the question of the best one-sided approximation of certain classes of continuous periodic functions by means of trigonometric polynomials of order ≤n-1 in the metric L2πp (1≤p<∞). Precise upper bounds are obtained for the best one-sided approximation of classes of 2π/n-periodic functions Hω,n [having arbitrary prescribed modulus of continuity ω(t)] in the metric L2πp, as well as of classes of 2π-periodic functions Hω [having prescribed modulus of continuity ω(t) with definite limits] in the metric L2π1.

Monotone approximation of certain classes of functions

Monotone approximation of certain classes of functions