Research Article

Set-valued solutions of an equation of Jensen type

Published in: Quaestiones Mathematicae
Volume 46 , issue 6 , 2023 , pages: 1237–1244

DOI: 10.2989/16073606.2022.2072249

Author(s): Alina Ramona Baias Technical University of Cluj-Napoca, Romania , Dorian Popa Technical University of Cluj-Napoca, Romania , Michael Th. Rassias Institute of Mathematics, University of Zurich, Switzerland

Keywords: Primary: 39B52 , Secondary: 54C60 , Set-valued map , Jensen equation , Popoviciu’s functional equation

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Abstract

In this paper we provide a characterization theorem for set-valued solutions of the functional equation for the case of compact, convex valued maps. We prove that every solution of the functional equation is the sum of an additive single-valued function and a nonempty compact and convex set.

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