Abstract
We construct a non-trivial set Φ of extended-real valued functions on ℝn, containing all affine functions, such that an extended-real valued function f on ℝn is convex if and only if it is Φ-convex in the sense of Dolecki and Kurcyusz, i.e., the (pointwise) supremum of some subset of Φ. Also, we prove a new sandwich theorem. Finally, we characterize the set of all extended-real valued functions on ℝn which are simultaneously convex and concave and we show that it contains properly the above set Φ. Hence, a function f on ℝn is convex if and only if it is the (pointwise) supremum of a set of simultaneously convex and concave functions. © 1998 Elsevier Science Inc. All rights reserved.
Original language | English |
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Pages (from-to) | 163-181 |
Journal | Linear Algebra and Its Applications |
Volume | 278 |
DOIs | |
Publication status | Published - 1 Jan 1998 |
Keywords
- Convex functions
- Generalized convexity
- Sandwich theorem