New types of continuities.
Nonlinear contractive conditions: A comparison and related problems
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,...
Note on a Theorem of Kuratowski-Sierpiński
Note on functions satisfying the integral Hölder condition
Given a modulus of continuity and then denotes the space of all functions with the period on that are locally integrable in power and whose integral modulus of continuity of power (see(1)) is majorized by a multiple of . The moduli of continuity are characterized for which contains “many” functions with infinite “essential” variation on an interval of length .
Nouvelle démonstration d'un théorème sur les fonctions discontinues