Opuscula Math. 30, no. 1 (), 53-60
http://dx.doi.org/10.7494/OpMath.2010.30.1.53
Opuscula Mathematica

# Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener

Abstract. We show that the one-sided regularizations of the generator of any uniformly continuous and convex compact valued composition operator, acting in the spaces of functions of bounded variation in the sense of Wiener, is an affine function.
Keywords: $$\varphi$$-variation in the sense of Wiener, set-valued functions, left and right regularizations, uniformly continuous composition (Nemytskii) operator, Jensen equation.
Mathematics Subject Classification: 47B33, 26B30, 26E25, 26B40.