The relevance of convex analysis for the study of monotonicity
β Scribed by Jean-Paul Penot
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 281 KB
- Volume
- 58
- Category
- Article
- ISSN
- 0362-546X
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In the paper we deal with the problem when the graph of the subdifferential operator of a convex lower semicontinuous function has a common point with the product of two convex nonempty weak and weak\* compact sets, i.e. when graph&j n (Q x Q\*) # 0. The results obtained partially solve the problem
proved that the function ΞΈ (x) defined by Ξ (x + 1) = β 2Ο (x/e) x e ΞΈ (x)/12x is strictly increasing for x β₯ 1. The aim of our work is to prove that -x -1 ΞΈ β²β²β² (x) is strictly completely monotonic on (0, β) . As direct consequences, we show that ΞΈ is strictly convex on (0, β) , and then we prove t