Series Approximation of Functions; Convergence of Series

AbstractIn this paper, we establish a new estimate for the degree of approximation of functions $f(x,y)$ f ( x , y ) belonging to the generalized Lipschitz class $Lip ((\xi _{1}, \xi _{2} );r )$ L i p ( ( ξ 1 , ξ 2 ) ; r ) , $r \geq 1$ r ≥ 1 , by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from $Lip ((\alpha ,\beta );r )$ L i p ( ( α , β ) ; r ) and $Lip(\alpha ,\beta )$ L i p ( α , β ) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and $(C, \gamma , \delta )$ ( C , γ , δ ) means.

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Asymptotic Behaviour of the Error of Polynomial Approximation of Functions Like $$\vert x\vert ^{{\alpha }+i{\beta }}$$

Computational Methods and Function Theory ◽

10.1007/s40315-021-00364-x ◽

2021 ◽

Author(s):

Michael I. Ganzburg

Keyword(s):

Asymptotic Behaviour ◽

Polynomial Approximation ◽

Approximation Of Functions ◽

Polynomial Approximation Of Functions

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Multivariate time series approximation by multiple trajectories of a dynamical system. Applications to internet traffic and COVID-19 data

10.1063/5.0033648 ◽

2020 ◽

Author(s):

V. Rayskin

Keyword(s):

Dynamical System ◽

Time Series ◽

Multivariate Time Series ◽

Internet Traffic ◽

Series Approximation

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Topological Completeness of Function Spaces Arising in the Hausdorff Approximation of Functions

Canadian Mathematical Bulletin ◽

10.4153/cmb-1992-058-1 ◽

1992 ◽

Vol 35 (4) ◽

pp. 439-448 ◽

Cited By ~ 3

Author(s):

Gerald Beer

Keyword(s):

Approximation Theory ◽

Metric Space ◽

Polish Space ◽

Complete Metric Space ◽

Approximation Of Functions ◽

Lower Envelopes ◽

Constructive Approximation ◽

Hausdorff Approximation ◽

Set Of Points ◽

Completely Metrizable

AbstractLet X be a complete metric space. Viewing continuous real functions on X as closed subsets of X × R, equipped with Hausdorff distance, we show that C(X, R) is completely metrizable provided X is complete and sigma compact. Following the Bulgarian school of constructive approximation theory, a bounded discontinuous function may be identified with its completed graph, the set of points between the upper and lower envelopes of the function. We show that the space of completed graphs, too, is completely metrizable, provided X is locally connected as well as sigma compact and complete. In the process, when X is a Polish space, we provide a simple answer to the following foundational question: which subsets of X × R arise as completed graphs?

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