Title  A POROSITY RESULT FOR A SADDLE POINT PROBLEM 
Publication Type  Journal Article 
Year of Publication  2006 
Authors  Zaslavski, AJ 
Secondary Title  Communications in Applied Analysis 
Volume  10 
Issue  1 
Start Page  9 
Pagination  17 
Date Published  01/2006 
Type of Work  scientific: mathematics 
ISSN  1083–2564 
AMS  49J35, 54E52 
Abstract  In this paper we consider a complete metric space M of functionsf : X × Y → R^{1} which satisfy ${ sup_{y∈Y} inf_{x∈X} f (x, y) = inf_{x∈X} sup_{y∈Y} f (x, y), }$ where ${X}$ and ${Y}$ are complete metric spaces. We establish that the set of all functions from M which have a unique saddle point has a σporous complement.

URL  http://www.acadsol.eu/en/articles/10/1/3.pdf 
Short Title  Saddle Point Problem 
Refereed Designation  Refereed 
Full Text  REFERENCES [1] J.P. Aubin and I. Ekeland, Applied Nonlinear Analysis, WileyInterscience, New York, 1984. [5] I. Ekeland and R.Temam, Analyse Convexe et Problemes Variationnels, Dunod, Paris, 1974. [6] S. Reich and A.J. Zaslavski, The set of divergent descent methods in a Banach space is σporous, SIAM J. Optim., 11 (2001), 10031018.
