Transformations which preserve convexity
Let C be the class of convex nondecreasing functions f:[0,∞)→[0,∞) which satisfy f(0)=0. Marshall and Proschan [1] determine the one-to-one and onto functions ψ:[0,∞)→[0,∞) such that g=ψ∘f∘ψ−1 belongs to C whenever f belongs to C. We study several natural models for multivariate extension of the Mar...
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| Format: | Article |
| Language: | English |
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Wiley
1985-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
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| Online Access: | http://dx.doi.org/10.1155/S0161171285000047 |
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| _version_ | 1849407971671408640 |
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| author | Robert A. Fontenot Frank Proschan |
| author_facet | Robert A. Fontenot Frank Proschan |
| author_sort | Robert A. Fontenot |
| collection | DOAJ |
| description | Let C be the class of convex nondecreasing functions f:[0,∞)→[0,∞) which satisfy f(0)=0. Marshall and Proschan [1] determine the one-to-one and onto functions ψ:[0,∞)→[0,∞) such that g=ψ∘f∘ψ−1 belongs to C whenever f belongs to C. We study several natural models for multivariate extension of the Marshall-Proschan result. We show that these result in essentially a restatement of the original Marshall-Proschan characterization. |
| format | Article |
| id | doaj-art-3f4e9d8c2f454ff2bf025bef9e6d290b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1985-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-3f4e9d8c2f454ff2bf025bef9e6d290b2025-08-20T03:35:54ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251985-01-0181495510.1155/S0161171285000047Transformations which preserve convexityRobert A. Fontenot0Frank Proschan1Department of Mathematics, Whitman College, Walla Walla, Washington 99362, USADepartment of Statistics, Florida State University, Tallahassee, Florida 32306, USALet C be the class of convex nondecreasing functions f:[0,∞)→[0,∞) which satisfy f(0)=0. Marshall and Proschan [1] determine the one-to-one and onto functions ψ:[0,∞)→[0,∞) such that g=ψ∘f∘ψ−1 belongs to C whenever f belongs to C. We study several natural models for multivariate extension of the Marshall-Proschan result. We show that these result in essentially a restatement of the original Marshall-Proschan characterization.http://dx.doi.org/10.1155/S0161171285000047convexitypreservation of convexitytransformations multivariatepermutation matrices. |
| spellingShingle | Robert A. Fontenot Frank Proschan Transformations which preserve convexity International Journal of Mathematics and Mathematical Sciences convexity preservation of convexity transformations multivariate permutation matrices. |
| title | Transformations which preserve convexity |
| title_full | Transformations which preserve convexity |
| title_fullStr | Transformations which preserve convexity |
| title_full_unstemmed | Transformations which preserve convexity |
| title_short | Transformations which preserve convexity |
| title_sort | transformations which preserve convexity |
| topic | convexity preservation of convexity transformations multivariate permutation matrices. |
| url | http://dx.doi.org/10.1155/S0161171285000047 |
| work_keys_str_mv | AT robertafontenot transformationswhichpreserveconvexity AT frankproschan transformationswhichpreserveconvexity |