On subdifferential in Hadamard spaces

Document Type : Research Paper


1 {School of Mathematics‎, ‎Statistics and Computer Science‎, ‎College of Science‎, ‎University of‎ ‎Tehran‎, ‎Enghelab Avenue‎, ‎Tehran‎, ‎Iran.

2 Department of Mathematics‎, ‎Faculty of Sciences‎, ‎Alzahra University‎, ‎Tehran‎, ‎Iran.


In this paper, we deal with the subdifferential concept on Hadamard spaces. Flat Hadamard spaces are characterized, and necessary and suficient conditions are presented to prove that the subdifferential set in Hadamard spaces is nonempty. Proximal subdifferential in Hadamard spaces is addressed and some basic properties are high-lighted. Finally, a density theorem for subdifferential set is established.


Main Subjects

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  • Receive Date: 13 September 2014
  • Revise Date: 05 April 2015
  • Accept Date: 06 April 2015
  • First Publish Date: 01 June 2016