
Journal of Convex Analysis 26 (2019), No. 2, 563572 Copyright Heldermann Verlag 2019 KMidconvex and KMidconcave SetValued Maps Bounded on "Large" Sets Eliza Jablonska Institute of Mathematics, Pedagogical University of Cracow, Podchorazych 2, 30084 Krakow, Poland elizajab0712@gmail.com Kazimierz Nikodem Dept. of Mathematics, University of BielskoBiala, ul. Willowa 2, 43309 BielskoBiala, Poland knikodem@ath.bielsko.pl We prove that every Kmidconvex setvalued map partially Kupper bounded on a "large" set (e.g. not nullfinite, not Haarnull or not Haarmeager set), as well as every Kmidconcave setvalued map Klower bounded on a "large" set, is Kcontinuous. These results generalize the solution of the problem posed by K. Baron and R. Ger [Problem P239, in: The 21st International Symposium on Functional Equations, Konolfingen (1983), Aequationes Math. 26 (1984) 225294], and also some results of K. Nikodem [Kconvex and Kconcave setvalued functions, Zeszyty Nauk. Politechniki Lodzkiej Mat. 559; Rozprawy Mat. 114, Lodz (1989)]. Keywords: Kmidconvex setvalued map, Kmidconcave setvalued map, Kcontinuity, nullfinite set, Haarnull set, Haarmeager set. MSC: 26B25; 39B62, 54C60 [ Fulltextpdf (98 KB)] for subscribers only. 