Milne-type inequalities for third differentiable and h-convex functions

This paper develops a novel Milne inequality for third-differentiable and h -convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p ≥ 1 for s -convexity, convexity, and P -functions class. We examine cases when the third derivativ...

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Bibliographic Details
Published in:Boundary value problems Vol. 2025; no. 1; pp. 4 - 15
Main Authors: Benaissa, Bouharket, Budak, Hüseyin
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 07.01.2025
Hindawi Limited
SpringerOpen
Subjects:
Analysis
Approximations and Expansions
Boundary value problems
Convex analysis
Convexity
Difference and Functional Equations
h-convex function
Hölder’s inequality
Inequalities
Mathematics
Mathematics and Statistics
Milne’s inequality
Ordinary Differential Equations
Partial Differential Equations
Riemann’s integral
Milne’s inequality
Hölder’s inequality
26A51
26D10
26A33
convex function
Riemann’s integral
26D15
ISSN:1687-2770, 1687-2762, 1687-2770
Online Access:Get full text
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Summary:This paper develops a novel Milne inequality for third-differentiable and h -convex functions using Riemann integrals. Furthermore, new Milne inequalities are proposed utilizing a summation parameter p ≥ 1 for s -convexity, convexity, and P -functions class. We examine cases when the third derivative functions are also bounded and Lipschitzian.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
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content type line 14
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-024-01984-7