Generalized Levinson's inequality and exponential convexity
We give a probabilistic version of Levinson's inequality under Mercer's assumption of equal variances for the family of 3-convex functions at a point. We also show that this is the largest family of continuous functions for which the inequality holds. New families of exponentially convex f...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2015-01-01
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| Series: | Opuscula Mathematica |
| Subjects: | |
| Online Access: | http://www.opuscula.agh.edu.pl/vol35/3/art/opuscula_math_3524.pdf |
| _version_ | 1818081971949010944 |
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| author | Josip Pečarić Marjan Praljak Alfred Witkowski |
| author_facet | Josip Pečarić Marjan Praljak Alfred Witkowski |
| author_sort | Josip Pečarić |
| collection | DOAJ |
| description | We give a probabilistic version of Levinson's inequality under Mercer's assumption of equal variances for the family of 3-convex functions at a point. We also show that this is the largest family of continuous functions for which the inequality holds. New families of exponentially convex functions and related results are derived from the obtained inequality. |
| first_indexed | 2024-12-10T19:14:41Z |
| format | Article |
| id | doaj.art-c5885bf78bb64efbaa3af0260bc88cef |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-10T19:14:41Z |
| publishDate | 2015-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-c5885bf78bb64efbaa3af0260bc88cef2022-12-22T01:36:37ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742015-01-01353397410http://dx.doi.org/10.7494/OpMath.2015.35.3.3973524Generalized Levinson's inequality and exponential convexityJosip Pečarić0Marjan Praljak1Alfred Witkowski2Faculty Of Textile Technology, University Of Zagreb, Prilaz baruna Filipovića 28a, 10000 Zagreb, CroatiaFaculty of Food Technology and Biotechnology, University Of Zagreb, Pierottijeva 6, 10000 Zagreb, CroatiaInstitute of Mathematics and Physics, UTP University of Science and Technology, al. prof. Kaliskiego 7, 85-796 Bydgoszcz, PolandWe give a probabilistic version of Levinson's inequality under Mercer's assumption of equal variances for the family of 3-convex functions at a point. We also show that this is the largest family of continuous functions for which the inequality holds. New families of exponentially convex functions and related results are derived from the obtained inequality.http://www.opuscula.agh.edu.pl/vol35/3/art/opuscula_math_3524.pdfLevinson's inequalityexponential convexity |
| spellingShingle | Josip Pečarić Marjan Praljak Alfred Witkowski Generalized Levinson's inequality and exponential convexity Opuscula Mathematica Levinson's inequality exponential convexity |
| title | Generalized Levinson's inequality and exponential convexity |
| title_full | Generalized Levinson's inequality and exponential convexity |
| title_fullStr | Generalized Levinson's inequality and exponential convexity |
| title_full_unstemmed | Generalized Levinson's inequality and exponential convexity |
| title_short | Generalized Levinson's inequality and exponential convexity |
| title_sort | generalized levinson s inequality and exponential convexity |
| topic | Levinson's inequality exponential convexity |
| url | http://www.opuscula.agh.edu.pl/vol35/3/art/opuscula_math_3524.pdf |
| work_keys_str_mv | AT josippecaric generalizedlevinsonsinequalityandexponentialconvexity AT marjanpraljak generalizedlevinsonsinequalityandexponentialconvexity AT alfredwitkowski generalizedlevinsonsinequalityandexponentialconvexity |