On the converse Jensen inequality for strongly convex functions

Counterparts of the converse Jensen inequality for strongly convex and strongly midconvex functions are presented. The Jessen inequality and converse Jessen inequality (involving linear positive normalized functionals) for strongly convex functions are also given.

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Published in:Journal of mathematical analysis and applications Vol. 434; no. 1; pp. 516 - 522
Main Authors: Klaričić Bakula, Milica, Nikodem, Kazimierz
Format: Journal Article
Language:English
Published: Elsevier Inc 01.02.2016
Subjects:
Converse Jensen inequality
Converse Jessen inequality
Jensen inequality
Jessen inequality
Strongly convex functions
Converse Jessen inequality
Strongly convex functions
Converse Jensen inequality
Jensen inequality
Jessen inequality
ISSN:0022-247X, 1096-0813
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Abstract Counterparts of the converse Jensen inequality for strongly convex and strongly midconvex functions are presented. The Jessen inequality and converse Jessen inequality (involving linear positive normalized functionals) for strongly convex functions are also given.
AbstractList Counterparts of the converse Jensen inequality for strongly convex and strongly midconvex functions are presented. The Jessen inequality and converse Jessen inequality (involving linear positive normalized functionals) for strongly convex functions are also given.
Author Nikodem, Kazimierz
Klaričić Bakula, Milica
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  givenname: Kazimierz
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  fullname: Nikodem, Kazimierz
  email: knikodem@ath.bielsko.pl
  organization: Department of Mathematics, University of Bielsko-Biala, ul. Willowa 2, 43-309 Bielsko-Biała, Poland
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Cites_doi 10.1016/j.amc.2011.12.037
10.7494/OpMath.2011.31.1.97
10.1090/S0002-9947-1945-0013169-9
10.15352/bjma/1313362982
10.7494/OpMath.2011.31.1.15
10.1070/SM1996v187n02ABEH000111
10.1016/0022-247X(85)90315-4
10.1007/s00010-010-0043-0
10.1090/S0002-9904-1937-06549-9
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Issue 1
Keywords Converse Jessen inequality
Strongly convex functions
Converse Jensen inequality
Jensen inequality
Jessen inequality
Language English
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SubjectTerms Converse Jensen inequality
Converse Jessen inequality
Jensen inequality
Jessen inequality
Strongly convex functions
Title On the converse Jensen inequality for strongly convex functions
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