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

详细

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 g_ε(τ, ξ) for which the least root ξ(τ) of the equation g_ε(τ, ξ) = 0 depends continuously on τ if ||g − g_ε||C < ε.