Some negative results for a monotonic approximation of a function that they have a fractional derivative of a complex order

Authors

DOI:

https://doi.org/10.17721/1812-5409.2024/1.20

Keywords:

approximation of the function, Sobolev space with a complex index, algebraic polynomial, monotone function, convex function

Abstract

The issue of interpolation approximation of functions from the Sobolev class by algebraic polynomials is considered. The question of monotone approximation is the question of approximation of monotone functions from the Sobolev class by monotone polynomials. This paper investigates the issue of monotone approximation in the Sobolev space with complex index r. This work is a generalization of previously obtained results for the case of Sobolev space with a real index.

Pages of the article in the issue: 101 - 104

Language of the article: Ukrainian

References

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DeVore R.A., Yu, X. M. (1985). Pointwise estimates for monotone polynomial approximation. Constr. Approx.№ 1, 323-331.

S. G. Samko, A. A. Kilbas, O. I. Marichev (1987). Fractional integrals and derivatives: theory and applications. Sci. Publ. - London.

Petrova T. O. (2003). On current interpolation estimates of the monotone approximation of functions with a fractional derivative. VISN. Kiev. UN-Tu. Math. Mechanics. № 9-10, 125-127. [in Ukrainian].

Petrova T. O. (2005). A counterexample in the interpolation convex approximation. Proceedings of the Institute of mathematics of the National Academy of Sciences of Ukraine "Mathematics and its application. Theory of approximation of functions 35, 107-112. [in Ukrainian].

Petrova T. O., Petrova I. L. generalization of current interpolation estimates of the convex approximation of functions having a fractional derivative. mathematical and computer modeling. Series: physical and Mathematical Sciences, 61-69.

Petrova T. O., One counterexample for the convex approximation of functions having a fractional derivative at r>4, Bulletin of the Taras Shevchenko National University of Kyiv. Series of physical and Mathematical Sciences. - 2018 - №3, 22-25.

Petrova T. O., On current interpolation estimates of the convex approximation of functions having a fractional derivative of arbitrary order, r є (3,4), Bulletin of Kiev University. Math. Mechanics 2(38) (2017), 9-10.

Petrova T. O., Petrova I. L., generalization of current interpolation estimates of convex approximation of functions with fractional derivative, mathematical and computer modeling. Series: physical and Mathematical Sciences, 61-69, 2019.

Petrova T. O., Petrova I. L., some negative results for interpolation monotone approximation of functions having a fractional derivative, Bulletin of the Taras Shevchenko National University of Kyiv. Series of physical and Mathematical Sciences. - 2020 - №3, 122-127.

Petrova T. O., Petrova I. L., generalization of negative results for the interpolation convex approximation of functions having a fractional derivative in Sobolev space, mathematical and computer modeling. Series: physical and Mathematical Sciences, 98-106.

Petrova T. O., Petrova I. L., generalization of negative results for interpolation monotonic approximation of functions having a fractional derivative in Sobolev space with the index r ∈ (2, 3), scientific Bulletin of Uzhgorod University. Series " Mathematics and Computer Science – Volume 42 №1 - 2023.

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Published

2024-09-12

How to Cite

Petrova, T. (2024). Some negative results for a monotonic approximation of a function that they have a fractional derivative of a complex order. Bulletin of Taras Shevchenko National University of Kyiv. Physical and Mathematical Sciences, 78(1), 101–104. https://doi.org/10.17721/1812-5409.2024/1.20

Issue

Vol. 78 No. 1 (2024)

Section

Differential equations, mathematical physics and mechanics

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Copyright (c) 2024 Tamara Petrova

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