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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References
I. E. Filippov and V. S. Mokeychev, “The least root of a continuous function,” Lobachevskii J. Math. 39, 200–203 (2018).
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(Submitted by A. M. Elizarov)
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Storozhuk, K.V. On the Article “The Least Root of a Continuous Function”. Lobachevskii J Math 39, 1445 (2018). https://doi.org/10.1134/S1995080218090457
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DOI: https://doi.org/10.1134/S1995080218090457