On e-monotonicity and maximality of operators in Banach spaces

Abstract In this paper we extend some well known properties of monotone and maximal monotone operators to the wider class of e -monotone and maximal e -monotone operators. The main results concern local boundedness of maximal e -monotone operators, maximal 2 e -monotonicity of the Clarke–Rockafellar subdifferential $$\partial ^{CR}f$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>∂</mml:mi> <mml:mrow> <mml:mi>CR</mml:mi> </mml:mrow> </mml:msup> <mml:mi>f</mml:mi> </mml:mrow> </mml:math> for an e -convex function f , and the characterization of e -monotonicity of an operator T via the behaviour of its e -Fitzpatrick function outside the graph of T .