Abstract

We show that a well-known property of monotone operators, namely local boundedness in the interior of their domain, remains valid for the larger class of premonotone maps. This generalizes a similar result by A. N. Iusem, G. Kassay and W. Sosa J. Convex Analysis 16 (2009) 807--826] to Banach spaces.

Author information

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

Mohammad Hossein Alizadeh

Dept. of Product and Systems Design Engineering, University of the Aegean, 84100 Hermoupolis, Syros, Greece

alizadeh@aegean.gr

Nicolas Hadjisavvas

Dept. of Product and Systems Design Engineering, University of the Aegean, 84100 Hermoupolis, Syros, Greece

nhad@aegean.gr

Mehdi Roohi

Dept. of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar 47416 -- 1468, Iran

m.roohi@umz.ac.ir

Keywords

  • Monotone operator
  • generalized monotone operator
  • locally bounded operator

Mathematics Subject Classification

47H05, 49J53, 47H04

Suggested citation

M. H. Alizadeh, N. Hadjisavvas, M. Roohi. “Local Boundedness Properties for Generalized Monotone Operators.” Journal of Convex Analysis 19 (2012), No. 1, 49–61.

Copyright Heldermann Verlag 2012