Necessary and sufficient conditions for discrete inequalities of Jensen–Steffensen type with applications

In this paper we give a necessary and sufficient condition for the discrete Jensen inequality to be satisfied for real (not necessarily nonnegative) weights. The result generalizes and completes the classical Jensen–Steffensen inequality. The validity of the strict inequality is studied. As applicat...

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Bibliographic Details
Published in:Journal of inequalities and applications Vol. 2024; no. 1; pp. 1 - 16
Main Author: Horváth, László
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 02.01.2024
Springer Nature B.V
SpringerOpen
Subjects:
Analysis
Applications of Mathematics
Convex and strongly convex functions
Discrete Jensen–Steffensen inequality
Mathematics
Mathematics and Statistics
Quasi-arithmetic means
Refinement
Refinement
Convex and strongly convex functions
Discrete Jensen–Steffensen inequality
Quasi-arithmetic means
ISSN:1029-242X, 1025-5834, 1029-242X
Online Access:Get full text
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Summary:In this paper we give a necessary and sufficient condition for the discrete Jensen inequality to be satisfied for real (not necessarily nonnegative) weights. The result generalizes and completes the classical Jensen–Steffensen inequality. The validity of the strict inequality is studied. As applications, we first give the form of our result for strongly convex functions, then we study discrete quasi-arithmetic means with real (not necessarily nonnegative) weights, and finally we refine the inequality obtained.
Bibliography:ObjectType-Article-1
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ISSN:1029-242X
1025-5834
1029-242X
DOI:10.1186/s13660-023-03073-2