A theorem on the extremum of a nonnegative bounded function

Using perturbation formulas for eigenvalues of linear operators, an equation is obtained for the extremal values of certain nonnegative bounded functions. Formulas are obtained for the derivative of regularizing maximal eigenvalues of matrices which depend on a parameter.Translated fromVychislitel'naya i Prikladnaya Matematika, No. 69, pp. 3–7, 1989.