On a Certain Generalized Functional Equation for Set-Valued Functions

Yaroslav Bazaykin, Dušan Bednařík, Veronika Borůvková and Tomáš Zuščák
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Yaroslav Bazaykin: Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic
Dušan Bednařík: Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic
Veronika Borůvková: Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic
Tomáš Zuščák: Department of Mathematics, Faculty of Science, University of Hradec Králové, 50003 Hradec Králové, Czech Republic

Mathematics, 2020, vol. 8, issue 12, 1-15

Abstract: The aim of the paper is to generalize results by Sikorska on some functional equations for set-valued functions. In the paper, a tool is described for solving a generalized type of an integral-functional equation for a set-valued function F : X → c c ( Y ) , where X is a real vector space and Y is a locally convex real linear metric space with an invariant metric. Most general results are described in the case of a compact topological group G equipped with the right-invariant Haar measure acting on X . Further results are found if the group G is finite or Y is Asplund space. The main results are applied to an example where X = R 2 and Y = R n , n ∈ N , and G is the unitary group U ( 1 ) .

Keywords: integral-functional equation; set-valued function; topological vector space; compact topological group (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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