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Journal of Convex Analysis 21 (2014), No. 4, 965--987
Copyright Heldermann Verlag 2014

Extension of Convex Function

Min Yan
Dept. of Mathematics, University of Science and Technology, Clear Water Bay, Hong Kong

We study the local and global versions of the convexity, which is closely related to the problem of extending a convex function on a non-convex domain to a convex function on the convex hull of the domain and beyond the convex hull. We also give the parallel results for the convexity defined by positive definite Hessian.

Keywords: Convex function, non-convex domain, convex hull, positive definite Hessian, extension.

MSC: 26B25

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