Fitzpatrick transform of monotone relations in Hadamard spaces

Abstract

In the present paper, monotone relations and maximal monotone relations from an Hadamard space to its linear dual space are investigated. Fitzpatrick transform of monotone relations in Hadamard spaces is introduced. It is shown that Fitzpatrick transform of a special class of monotone relations is proper, convex and lower semi-continuous. Finally, a representation result for monotone relations is given.

Keywords

• monotone relations
• hadamard spaces
• flat hadamard spaces
• ℝ-tree space
• fitzpatrick transform
• primary 47h05
• secondary 47h04