Nonlinear best Chebyshev approximations and splines

The necessity of using parametric nonlinear expressions and splines arises because real physical processes are described by many different analytical dependencies. The classic technique of finding the best Chebyshev approximation is also based on nonlinear approximations. But such approximations are not always possible. The author formulates a theorem that allows one to establish the condition of existence of the best Chebyshev approximation of a chosen kind.