Set-valued solutions of an equation of Jensen type
Alina Ramona Baias, Dorian Popa, Michael Th. Rassias
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.
Topics & Concepts
MathematicsFunctional equationCompact spaceCharacterization (materials science)Regular polygonSet (abstract data type)Type (biology)Convex setSolution setSet functionPure mathematicsSubderivativeFunction (biology)Convex analysisDiscrete mathematicsMathematical analysisConvex optimizationDifferential equationComputer scienceBiologyEvolutionary biologyMaterials scienceGeometryNanotechnologyEcologyProgramming languageFunctional Equations Stability ResultsFixed Point Theorems AnalysisFuzzy Systems and Optimization