On the implicit function theorem for Lipschitz mappings

New estimations for Lipschitz constant of solutions in the Clarke’s implicit function theorem are proved. Let = 𝑥0(𝑟1) ⊂ R𝑛, = 𝑦0(𝑟2) ⊂ R𝑚 and : 𝑈×𝑉 → R𝑚 be a local Lipschitz mapping in some neighbourhood of point (𝑥0, 𝑦0). Let 𝜕𝑦𝐹(𝑥0, 𝑦0) is of maximal rank. Then for every Δ*, Δ