%0 Journal Article
%T Monotone Linear Relations: Maximality and Fitzpatrick Functions
%A Heinz H. Bauschke
%A Xianfu Wang
%A Liangjin Yao
%J Mathematics
%D 2008
%I arXiv
%X We analyze and characterize maximal monotonicity of linear relations (set-valued operators with linear graphs). An important tool in our study are Fitzpatrick functions. The results obtained partially extend work on linear and at most single-valued operators by Phelps and Simons and by Bauschke, Borwein and Wang. Furthermore, a description of skew linear relations in terms of the Fitzpatrick family is obtained. We also answer one of Simons problems by showing that if a maximal monotone operator has a convex graph, then this graph must actually be affine.
%U http://arxiv.org/abs/0805.4256v1