Journal of Convex Analysis 19 (2012), No. 1, 049--061
Copyright Heldermann Verlag 2012
Local Boundedness Properties for Generalized Monotone Operators
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
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.
Keywords: Monotone operator, generalized monotone operator, locally bounded operator.
MSC: 47H05, 49J53, 47H04
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