TY - JOUR

T1 - On the Article “The Least Root of a Continuous Function”

AU - Storozhuk, K. V.

PY - 2018/11/1

Y1 - 2018/11/1

N2 - 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.

AB - 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.

KW - continuity

KW - Implicit function

KW - zeros of functions

UR - http://www.scopus.com/inward/record.url?scp=85059682568&partnerID=8YFLogxK

U2 - 10.1134/S1995080218090457

DO - 10.1134/S1995080218090457

M3 - Article

AN - SCOPUS:85059682568

VL - 39

SP - 1445

EP - 1445

JO - Lobachevskii Journal of Mathematics

JF - Lobachevskii Journal of Mathematics

SN - 1995-0802

IS - 9

ER -