The Least Root of a Continuous Function
- Authors: Filippov I.E.1, Mokeychev V.S.1
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Affiliations:
- Kazan (Volga Region) Federal University
- Issue: Vol 39, No 2 (2018)
- Pages: 200-203
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/201383
- DOI: https://doi.org/10.1134/S1995080218020117
- ID: 201383
Cite item
Abstract
For each ε > 0 and each scalar real valued and continuous on a compact set Ω ⊂ Rn, ξ ∈ [a, b] function g(τ, ξ) such that g(τ, a) · g(τ, b) < 0 we construct a function gε(τ, ξ), for which the least root ξ(τ) of the equation gε(τ, ξ) = 0 continuously depends on τ, while |g(τ, ξ) − gε(τ, ξ)| < ε. We give examples illustrating the fact that in a general case assumptions are unimprovable.
Keywords
About the authors
I. E. Filippov
Kazan (Volga Region) Federal University
Author for correspondence.
Email: Igor.Filippov@kpfu.ru
Russian Federation, ul. Kremlevskaya 35, Kazan, Tatarstan, 420008
V. S. Mokeychev
Kazan (Volga Region) Federal University
Email: Igor.Filippov@kpfu.ru
Russian Federation, ul. Kremlevskaya 35, Kazan, Tatarstan, 420008