IJPAM: Volume 20, No. 1 (2005)

ON THE MORDUKHOVICH SUBDIFFERENTIAL
IN BINORMED SPACES AND SOME APPLICATIONS

S. Lahrech$^1$, A. Benbrik$^2$
$^{1,2}$Department of Mathematics
Faculty of Science
Mohamed First University
Oujda, 60000, MOROCCO
$^1$e-mail: lahrech@sciences.univ-oujda.ac.ma
$^2$e-mail: benbrik@sciences.univ-oujda.ac.ma


Abstract.The limiting subdifferential was first studied by Mordukhovich in [#!M1!#], followed by joint work with Kruger in [#!K!#], and by work of Ioffe [#!A1!#,#!A2!#].

The power of the limiting subdifferential as a tool in recognizing metric regularity was first observed by Mordukhovich [#!M2!#]. Using the limiting subdifferential, he presented a convenient test for the metric regularity of strictly differentiable mappings in terms of the adjoint of its strict derivative.

In this paper, we give a test for the metric regularity of non necessarily strictly differentiable mappings using the notion of Mordukhovich subdifferentiability in binormed spaces. This result strengthens and generalizes the elegant result of Mordukhovich.

Finally, we give an example of non strictly differentiable mapping for which the given test works.

Received: February 17, 2005

AMS Subject Classification: 49J52, 49J50

Key Words and Phrases: metric regularity, Mordukhovich subdifferential in binormed spaces, strictly Taylor differentiable mappings, closed pair of multifunctions

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 1