The Experts below are selected from a list of 3 Experts worldwide ranked by ideXlab platform
Jon D. Vanderwerff - One of the best experts on this subject based on the ideXlab platform.
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Epigraphical and Uniform Convergence of Convex Functions
1995Co-Authors: Jonathan M. Borwein, Jon D. VanderwerffAbstract:. We examine when a sequence of Lsc Convex Functions on a Banach space converges uniformly on bounded sets (resp. compact sets) provided it converges Attouch-Wets (resp. Painlev'e-Kuratowski). We also obtain related results for pointwise convergence and uniform convergence on weakly compact sets. Some known results concerning the convergence of sequences of linear Functionals are shown to also hold for Lsc Convex Functions. For example, a sequence of Lsc Convex Functions converges uniformly on bounded sets to a continuous affine Function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of ` 1 . y Research supported in part by an NSERC research grant and by the Shrum endowment. AMS Classification. 46A55, 46B20, 52A41. Key Words: Epi-convergence, Lsc Convex Function, uniform convergence, pointwise convergence, Attouch-Wets convergence, Painlev'e-Kuratowski convergence, Mosco convergence. 2 Borwein and Vanderwerff Intro..
Jonathan M. Borwein - One of the best experts on this subject based on the ideXlab platform.
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Epigraphical and Uniform Convergence of Convex Functions
1995Co-Authors: Jonathan M. Borwein, Jon D. VanderwerffAbstract:. We examine when a sequence of Lsc Convex Functions on a Banach space converges uniformly on bounded sets (resp. compact sets) provided it converges Attouch-Wets (resp. Painlev'e-Kuratowski). We also obtain related results for pointwise convergence and uniform convergence on weakly compact sets. Some known results concerning the convergence of sequences of linear Functionals are shown to also hold for Lsc Convex Functions. For example, a sequence of Lsc Convex Functions converges uniformly on bounded sets to a continuous affine Function provided that the convergence is uniform on weakly compact sets and the space does not contain an isomorphic copy of ` 1 . y Research supported in part by an NSERC research grant and by the Shrum endowment. AMS Classification. 46A55, 46B20, 52A41. Key Words: Epi-convergence, Lsc Convex Function, uniform convergence, pointwise convergence, Attouch-Wets convergence, Painlev'e-Kuratowski convergence, Mosco convergence. 2 Borwein and Vanderwerff Intro..
