scholarly journals On degree of approximation of function by Voronoi means of its Fourier integral

2021 ◽  
Vol 19 ◽  
pp. 24
Author(s):  
L.G. Bojtsun ◽  
T.I. Rybnikova
Keyword(s):  
Continuous Function ◽  
Fourier Integral ◽  
Degree Of Approximation ◽  
Approximation Of Function

The theorem on the degree of approximation to continuous function $f(x) \in L(-\infty; \infty)$ by Voronoi means of its Fourier integral is proved.

scholarly journals One counterexample for convex approximation of function with fractional derivatives, r>4

2018 ◽  
pp. 53-56
Author(s):  
T. Petrova
Keyword(s):  
Convex Function ◽  
Algebraic Polynomial ◽  
Fractional Derivatives ◽  
Nondecreasing Function ◽  
Degree Of Approximation ◽  
Monotone Approximation ◽  
Convex Approximation ◽  
Positive Functions ◽  
Approximation Of A Function ◽  
Approximation Of Function

We discuss whether on not it is possible to have interpolatory estimates in the approximation of a function f \in W^r [0,1] by polynomials. The problem of positive approximation is to estimate the pointwise degree of approximation of a function f \in C^r [0,1] \Wedge \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 \in N, r>2. In [8] is consider r \in R, r>2. It was proved that for monotone approximation estimates of the form (1) are fails for r \in R, 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],[11]). In [5] is consider r \in N, r>2. It was proved that for convex approximation estimates of the form (1) are fails for r \in N, r>2. In [6] is consider r \in R, r\in(2;3). It was proved that for convex approximation estimates of the form (1) are fails for r \in R, r\in(2;3). In [11] is consider r \in R, r\in(3;4). It was proved that for convex approximation estimates of the form (1) are fails for r \in R, r\in(3;4). In [9] is consider r \in R, r>4. It was proved that for f \in W^r [0,1] \Wedge \Delta^2, r>4 estimate (1) is not true. In this paper the question of approximation of function f \in W^r [0,1] \Wedge \Delta^2, r>4 by algebraic polynomial p_n \in \Pi_n \Wedge \Delta^2 is consider. It is proved, that for f \in W^r [0,1] \Wedge \Delta^2, r>4, estimate (1) can be improved, generally speaking.

On degree of approximation of function V

2017 ◽  
Vol 11 (22) ◽  
pp. 1075-1079
Author(s):  
Anwar Habib
Keyword(s):  
Degree Of Approximation ◽  
Bernstein Type ◽  
Approximation Of Function

We have defined a new Bernstein type polynomial.

scholarly journals On the Degree of Approximation of a Function by Nörlund Means of its Fourier Laguerre Series

2020 ◽  
Vol 1 ◽  
pp. 65-70
Author(s):  
Suresh Kumar Sahani ◽  
Vishnu Narayan Mishra ◽  
Narayan Prasad Pahari
Keyword(s):  
Degree Of Approximation ◽  
End Point ◽  
Laguerre Series ◽  
Nörlund Means ◽  
The Given ◽  
Approximation Of A Function ◽  
Approximation Of Function

In this paper, we have proved the degree of approximation of function belonging to L[0, ∞) by Nörlund Summability of Fourier-Laguerre series at the end point x = 0. The purpose of this paper is to concentrate on the approximation relations of the function in L[0, ∞) by Nörlund Summability of Fourier- Laguerre series associate with the given function motivated by the works [3], [9] and [13].  

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