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

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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.

Original languageEnglish
Pages (from-to)1445-1445
Number of pages1
JournalLobachevskii Journal of Mathematics
Issue number9
Publication statusPublished - 1 Nov 2018


  • continuity
  • Implicit function
  • zeros of functions


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