Local Boundedness Properties for Generalized Monotone Operators

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.