Małgorzata Wróbel

Uniformly bounded set-valued Nemytskij operators acting between generalized Hölder function spaces

We show that the generator of any uniformly bounded set-valued Nemytskij composition operator acting between generalized Hölder function metric spaces, with nonempty, bounded, closed, and convex values, is an affine function.

A Generalization of m-Convexity and a Sandwich Theorem

Abstract Functional inequalities generalizing m-convexity are considered. A result of a sandwich type is proved. Some applications are indicated.

ON A SPECIAL CASE OF THE GOLAB-SCHINZEL FUNCTIONAL EQUATION

The Gol^b-Schinzel functional equation (1) f(x + yf(x)) = f ( x ) f ( y ) , where / : R —• R, was considered by many authors (see for instance (1)-[4]). There are known the solutions of the equation (1). Among other, if / : R —• R is bijective, then f ( x ) = 1 + cx, x 6 R, where c is an arbitrary constant. In the present paper we investigate the Golq,b-Schinzel functional equation restricted to the diagonal, i.e., the functional equation in a single variable of the form (2) f(x + xf(x)) = [f(x)], xeR. Let / : R —• R be bijective. Inserting / 1 ( a ; ) instead of x, we have / 1 ( a ; ) + xf~(x) = f~(x), and putting