Lobachevskii Journal of Mathematics

, Volume 39, Issue 9, pp 1445–1445 | Cite as

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

  • K. V. StorozhukEmail author
Part 2. Special issue “Actual Problems of Algebra and Analysis” Editors: A. M. Elizarov and E. K. Lipachev


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 ||ggε||C < ε.

Keywords and phrases

Implicit function continuity zeros of functions 


  1. 1.
    I. E. Filippov and V. S. Mokeychev, “The least root of a continuous function,” Lobachevskii J. Math. 39, 200–203 (2018).MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Sobolev Institute of MathematicsNovosibirskRussia
  2. 2.Novosibirsk State UniversityNovosibirskRussia

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