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On the Article “The Least Root of a Continuous Function”. / Storozhuk, K. V.

In: Lobachevskii Journal of Mathematics, Vol. 39, No. 9, 01.11.2018, p. 1445-1445.

Research output: Contribution to journal › Article › peer-review

Harvard

Storozhuk, KV 2018, 'On the Article “The Least Root of a Continuous Function”', Lobachevskii Journal of Mathematics, vol. 39, no. 9, pp. 1445-1445. https://doi.org/10.1134/S1995080218090457

APA

Storozhuk, K. V. (2018). On the Article “The Least Root of a Continuous Function”. Lobachevskii Journal of Mathematics, 39(9), 1445-1445. https://doi.org/10.1134/S1995080218090457

Vancouver

Storozhuk KV. On the Article “The Least Root of a Continuous Function”. Lobachevskii Journal of Mathematics. 2018 Nov 1;39(9):1445-1445. doi: 10.1134/S1995080218090457

Author

Storozhuk, K. V. / On the Article “The Least Root of a Continuous Function”. In: Lobachevskii Journal of Mathematics. 2018 ; Vol. 39, No. 9. pp. 1445-1445.

BibTeX

@article{ae7225fddfe548648b6d801faee3dd89,
title = "On the Article “The Least Root of a Continuous Function”",
abstract = "We give a counterexample to the following assertion from article I.E. Filippov and V.S. Mokeychev. The Least Root of a Continuous Function. Lobachevskii Journal of Mathematics, 2018, V. 39, No 2, P. 200–203: for every ε > 0 and every function g(τ, ξ) ∈ ℝ, ξ ∈ [a, b], continuous on a compact set Ω ⊂ ℝn and such that g(τ, a) · g(τ, b) < 0, there exist a function gε(τ, ξ) for which the least root ξ(τ) of the equation gε(τ, ξ) = 0 depends continuously on τ if ||g − gε||C < ε.",
keywords = "continuity, Implicit function, zeros of functions",
author = "Storozhuk, {K. V.}",
year = "2018",
month = nov,
day = "1",
doi = "10.1134/S1995080218090457",
language = "English",
volume = "39",
pages = "1445--1445",
journal = "Lobachevskii Journal of Mathematics",
issn = "1995-0802",
publisher = "Maik Nauka Publishing / Springer SBM",
number = "9",

}

RIS

TY - JOUR

T1 - On the Article “The Least Root of a Continuous Function”

AU - Storozhuk, K. V.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - We give a counterexample to the following assertion from article I.E. Filippov and V.S. Mokeychev. The Least Root of a Continuous Function. Lobachevskii Journal of Mathematics, 2018, V. 39, No 2, P. 200–203: for every ε > 0 and every function g(τ, ξ) ∈ ℝ, ξ ∈ [a, b], continuous on a compact set Ω ⊂ ℝn and such that g(τ, a) · g(τ, b) < 0, there exist a function gε(τ, ξ) for which the least root ξ(τ) of the equation gε(τ, ξ) = 0 depends continuously on τ if ||g − gε||C < ε.

AB - We give a counterexample to the following assertion from article I.E. Filippov and V.S. Mokeychev. The Least Root of a Continuous Function. Lobachevskii Journal of Mathematics, 2018, V. 39, No 2, P. 200–203: for every ε > 0 and every function g(τ, ξ) ∈ ℝ, ξ ∈ [a, b], continuous on a compact set Ω ⊂ ℝn and such that g(τ, a) · g(τ, b) < 0, there exist a function gε(τ, ξ) for which the least root ξ(τ) of the equation gε(τ, ξ) = 0 depends continuously on τ if ||g − gε||C < ε.

KW - continuity

KW - Implicit function

KW - zeros of functions

UR - http://www.scopus.com/inward/record.url?scp=85059682568&partnerID=8YFLogxK

U2 - 10.1134/S1995080218090457

DO - 10.1134/S1995080218090457

M3 - Article

AN - SCOPUS:85059682568

VL - 39

SP - 1445

EP - 1445

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 9

ER -

ID: 18073569