O nierównościach funkcyjnych jednej zmiennej

Abstract

In this paper we shall deal with functional inequality (0.1). The main results are given in paragraph 2, where the algebraic structur of the family of solutions is given, and in paragraph 4, where a comparison theorem is proved for inequality (0.1) see theorem (4.1). In the same paragraph, there is a necessary and sufficient condition given for a function satisfying inequality (0.1) to be a continuous solution of equation (0.3). In paragraph 3, we have studied more exactly the homogeneous inequality (inequality 3.1). The last theorem in the paper gives the iseomorphism between the family of continuous solutions of inequality (0.1) and the family of continuous functions f-decreasing (see definition 3.2).