This work concerns generalized convex real-valued functions defined on a nonempty convex subset of a real topological linear space. Its aim is twofold: first, to show that any local maximum point of an explicitly quasiconvex function is a global minimum point whenever it belongs to the intrinsic core of the function’s domain and second, to characterize strictly convex normed spaces by applying this property for a particular class of convex functions.
Local maximum point Relative algebraic interior Convex function Explicitly quasiconvex function Strictly convex space Least squares problem
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Nicolae Popovici’s research was supported by CNCS-UEFISCDI, within the project PN-II-ID-PCE-2011-3-0024. The authors wish to thank professor Valeriu Anisiu for suggesting them to investigate whether Corollary 4.1 could be used in order to characterize the class of strictly convex normed spaces, which led to Corollary 4.2. They are also grateful to the referee whose valuable comments and suggestions improved the paper.
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