Opuscula Math. 30, no. 1 (2010), 53-60
Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener
A. Azócar
J. A. Guerrero
J. Matkowski
N. Merentes
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.
About the authors ▼
A. Azócar
Universidad Nacional Abierta, Area de Matemática Caracas, Venezuela
J. A. Guerrero
Universidad Nacional Experimental del Táchira, Dpto. de Matemáticas y Física, San Cristóbal, Venezuela
J. Matkowski
University of Zielona Góra, Institute of Mathematics, Computer Science and Econometrics, ul. Podgórna 50, 65-246 Zielona Góra, Poland; Silesian University, Institute of Mathematics, ul. Bankowa 14, 40-007, Katowice, Poland
N. Merentes
Universidad Central de Venezuela, Escuela de Matemáticas Caracas, Venezuela
About the article ▼
Received: 2009-09-18.
Revised: 2009-10-07.
Accepted: 2009-10-07.
Cite this article as ▼
A. Azócar, J. A. Guerrero, J. Matkowski, N. Merentes, Uniformly continuous set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener, Opuscula Math. 30, no. 1 (2010), 53-60,
http://dx.doi.org/10.7494/OpMath.2010.30.1.53.
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