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Set-Valued Anal (2008) 16:581596 DOI 10.1007/s11228-007-0053-9
 

Summary: Set-Valued Anal (2008) 16:581­596
DOI 10.1007/s11228-007-0053-9
Fixed Points and Zeros for Set Valued Mappings
on Riemannian Manifolds: A Subdifferential Approach
Daniel Azagra · Juan Ferrera · Beatriz Sanz
Received: 2 October 2006 / Accepted: 18 June 2007 /
Published online: 24 July 2007
© Springer Science + Business Media B.V. 2007
Abstract In this paper we establish several results which allow to find fixed points
and zeros of set-valued mappings on Riemannian manifolds. In order to prove
these results we make use of subdifferential calculus. We also give some useful
applications.
Keywords Fixed point · Set valued mapping · Subdifferential · Graphical derivative
Mathematics Subject Classifications (2000) 49J52 · 49J53 · 58C30
1 Introduction
It is well known that graphical derivatives of set-valued mappings can be very useful
in order to obtain fixed-point and inverse-function-like results. We could cite [1]
for instance, where a calculus of contingent derivatives is introduced and applied
to prove an adaptation of the inverse function theorem due to Ekeland (which we
generalize here to the setting of Riemannian manifolds, see Theorem 10 below).

  

Source: Azagra Rueda, Daniel - Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid

 

Collections: Mathematics