On the maximal monotone operators in Hadamard spaces

Abstract

In this paper, some topics of monotone operator theory in the setting of Hadamard spaces are investigated. For a fixed element p in a Hadamard space X, the notion of p-Fenchel conjugate is introduced and a type of the Fenchel-Young inequality is proved. Moreover, we examine the p-Fitzpatrick transform and its main properties for monotone set-valued operators in Hadamard spaces. Furthermore, some relations between maximal monotone operators and certain classes of proper, convex, l.s.c. extended real-valued functions on X × X ◊ , are given.