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Journal of Convex Analysis 11 (2004), No. 1, 197--208
Copyright Heldermann Verlag 2004
An Epi-Convergence Result for Bivariate Convex Functions
Adib Bagh
Dept. of Economics, University of California, One Shields Avenue, Davis, CA 95616, U.S.A.,
bagh@math.ucdavis.edu
We prove that for a large class of convex and lower semi-continuous biavariate
functions defined over RN, epi-convergence in one variable implies
epi-convergence in both variables. We also show that for closed-valued and
graph-convex mappings with domains with non empty interiors, pointwise
convergence implies graph convergence. We provide a number of applications
for both results.
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