On the qualitative approximation of Lipschitzian functions Original Research Article

Problem of topological equivalence between a function and certain local approximations is studied. The study is carried out in a neighbourhood of a critical point with the concept of critical point of Clarkeʹs theory. The function belongs to a particular class of non B-differentiable functions. The local approximations are positively homogeneous maps. Using the concept of topological equivalence we establish the existence of a local coordinate transformation between the original function and the positively homogeneous function. As a consequence we obtain sufficient conditions for the existence of local extremes for the initial map.