Email this article On the Article “The Least Root of a Continuous Function”
- Authors: Storozhuk K.V.1,2
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Affiliations:
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 39, No 9 (2018)
- Pages: 1445-1445
- Section: Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev
- URL: https://journals.rcsi.science/1995-0802/article/view/203603
- DOI: https://doi.org/10.1134/S1995080218090457
- ID: 203603
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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.
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About the authors
K. V. Storozhuk
Sobolev Institute of Mathematics; Novosibirsk State University
Author for correspondence.
Email: stork@math.nsc.ru
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 1, Novosibirsk, 630090
