Strong F-convexity and concavity and refinements of some classical inequalities

The concept of strong F -convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong F -concavity. Usin...

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Published inJournal of inequalities and applications Vol. 2024; no. 1; p. 96
Main Author Perić, Jurica
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.12.2024
Springer Nature B.V
Subjects
Analysis
Applications of Mathematics
Concavity
Convex analysis
Convexity
Inequalities
Mathematical functions
Mathematics
Mathematics and Statistics
Lah
26A51
Young inequality
Strong concavity
concavity
Strong
Reversed Young inequality
Jensen inequality
Ribarič inequality
26D15
Online AccessGet full text
ISSN1025-5834
1029-242X
DOI10.1186/s13660-024-03178-2

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Abstract The concept of strong F -convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong F -concavity. Using this concept, refinements of the Young inequality are given as a model case. A general form of the self-improving property for Jensen type inequalities is presented. We show that a careful choice of control functions for convex or concave functions can give a control over these refinements and produce refinements of the power mean inequalities.
AbstractList The concept of strong F-convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong F-concavity. Using this concept, refinements of the Young inequality are given as a model case. A general form of the self-improving property for Jensen type inequalities is presented. We show that a careful choice of control functions for convex or concave functions can give a control over these refinements and produce refinements of the power mean inequalities.
The concept of strong F -convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show that in more effective and specific analysis this concept is very useful, and especially its generalization, namely strong F -concavity. Using this concept, refinements of the Young inequality are given as a model case. A general form of the self-improving property for Jensen type inequalities is presented. We show that a careful choice of control functions for convex or concave functions can give a control over these refinements and produce refinements of the power mean inequalities.
Author Perić, Jurica
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Cites_doi 10.1186/s13660-023-02934-0
10.1016/j.jmaa.2015.09.032
10.1007/s00025-021-01460-z
10.1007/0-387-31077-0
10.1007/978-94-017-1043-5
10.1016/j.jmaa.2023.127866
10.1007/s00010-010-0043-0
10.1007/s41980-018-0095-9
10.1186/s13660-020-02369-x
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Keywords Lah
26A51
Young inequality
Strong concavity
concavity
Strong
Reversed Young inequality
Jensen inequality
Ribarič inequality
26D15
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Pečarić, Perić (CR14) 2020; 2020
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Klaričić, Nikodem (CR6) 2016; 434
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Snippet The concept of strong F -convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show...
The concept of strong F-convexity is a natural generalization of strong convexity. Although strongly concave functions are rarely mentioned and used, we show...
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SubjectTerms Analysis
Applications of Mathematics
Concavity
Convex analysis
Convexity
Inequalities
Mathematical functions
Mathematics
Mathematics and Statistics
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Title Strong F-convexity and concavity and refinements of some classical inequalities
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