Lobachevskii Journal of Mathematics

, Volume 39, Issue 2, pp 200–203 | Cite as

The Least Root of a Continuous Function

  • I. E. Filippov
  • V. S. Mokeychev


For each ε > 0 and each scalar real valued and continuous on a compact set Ω ⊂ R n , 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 and phrases

Implicit functions continuousness zeros of functions 


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Copyright information

© Pleiades Publishing, Ltd. 2018

Authors and Affiliations

  1. 1.Kazan (Volga Region) Federal UniversityKazan, TatarstanRussia

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