Abstract

Recently, C. Zalinescu ["A new convexity property for monotone operators", Journal of Convex Analysis 13 (2006) 883--887] posed a question about the characterization of the intrinsic core of the Minkowski sum of two graphs associated with two maximal monotone operators. In this note we give an affirmative answer.

Author information

Contact details are reproduced from the original publication and may be historical.

Liangjin Yao

Dept. of Mathematics, Irving K. Barber School, University of Britisch Columbia, Okanagan - Kelowna BC, Canada V1V 1V7

ljinyao@interchange.ubc.ca

Keywords

  • Convex function
  • convex set
  • Fenchel conjugate
  • Fitzpatrick function
  • intrinsic core
  • maximal monotone operator
  • monotone operator
  • multifunction
  • relative algebraic interior
  • representative
  • set-valued operator

Mathematics Subject Classification

47H05; 49J53, 52A41

Suggested citation

L. Yao. “An affirmative answer to a problem posed by Zalinescu.” Journal of Convex Analysis 18 (2011), No. 3, 621–626.

Copyright Heldermann Verlag 2011