Opuscula Math. 30, no. 1 (2010), 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

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.

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  • 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
  • Received: 2009-09-18.
  • Revised: 2009-10-07.
  • Accepted: 2009-10-07.
Opuscula Mathematica - cover

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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