n-Convex Functions in Linear Spaces.
We give some necessary and sufficient conditions for an n-1 times differentiable function to be a generalized convex function with respect to an unrestricted n-parameter family.
We establish five theorems giving lists of nonlinear contractive conditions which turn out to be mutually equivalent. We derive them from some general lemmas concerning subsets of the plane which may be applied both in the single- or set-valued case as well as for a family of mappings. A separation theorem for concave functions is proved as an auxiliary result. Also, we discuss briefly the following problems for several classes of contractions: stability of procedure of successive approximations,...