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

Janusz Matkowski; Małgorzata Wróbel — 2012

Open Mathematics

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.

Uniformly bounded Nemytskij operators generated by set-valued functions between generalized Hölder function spaces

Janusz Matkowski; Małgorzata Wróbel — 2011

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

We prove that the generator of any uniformly bounded set-valued Nemytskij operator acting between generalized Hölder function metric spaces, with nonempty compact and convex values is an affine function with respect to the function variable.

A Generalization of m-Convexity and a Sandwich Theorem

Teodoro Lara; Janusz Matkowski; Nelson Merentes; Roy Quintero; Małgorzata Wróbel — 2017

Annales Mathematicae Silesianae

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

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