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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Vydáno v:	Boundary value problems Ročník 2025; číslo 1; s. 4 - 15
Hlavní autoři:	Benaissa, Bouharket, Budak, Hüseyin
Médium:	Journal Article
Jazyk:	angličtina
Vydáno:	Cham Springer International Publishing 07.01.2025 Hindawi Limited SpringerOpen
Témata:	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
On-line přístup:	Získat plný text
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Shrnutí:	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.
Bibliografie:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-024-01984-7