Vol. 276, No. 2, 2015

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ISSN: 0030-8730
On the density theorem for the subdifferential of convex functions on Hadamard spaces

Mina Movahedi, Daryoush Behmardi and Seyedehsomayeh Hosseini

Vol. 276 (2015), No. 2, 437–447
Abstract

We introduce a dual space for any geodesically complete Hadamard space. By using this notion we give a new definition of the subdifferential of convex functions on geodesically complete Hadamard spaces. Some properties of this subdifferential, such as a density theorem, are proved.

Keywords
Hadamard spaces, convex functions, subdifferential
Mathematical Subject Classification 2010
Primary: 53C23
Secondary: 47H05
Milestones
Received: 30 April 2014
Revised: 19 January 2015
Accepted: 2 February 2015
Published: 15 July 2015
Authors
Mina Movahedi
Department of Mathematics
Faculty of Sciences
Alzahra University
Tehran
Iran
Daryoush Behmardi
Department of Mathematics
Faculty of Sciences
Alzahra University
Tehran
Iran
Seyedehsomayeh Hosseini
Seminar of Applied Mathematics
Eidgenössische Technische Hochschule
CH-8092 Zürich
Switzerland