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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| Published in: | Boundary value problems Vol. 2025; no. 1; pp. 4 - 15 |
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| Main Authors: | , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Cham
Springer International Publishing
07.01.2025
Hindawi Limited SpringerOpen |
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| ISSN: | 1687-2770, 1687-2762, 1687-2770 |
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| Abstract | 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. |
|---|---|
| AbstractList | 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. 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. Abstract 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 $p\geq 1$ for s-convexity, convexity, and P-functions class. We examine cases when the third derivative functions are also bounded and Lipschitzian. |
| ArticleNumber | 4 |
| Author | Budak, Hüseyin Benaissa, Bouharket |
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| Snippet | This paper develops a novel Milne inequality for third-differentiable and
h
-convex functions using Riemann integrals. Furthermore, new Milne inequalities are... This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne inequalities are... Abstract This paper develops a novel Milne inequality for third-differentiable and h-convex functions using Riemann integrals. Furthermore, new Milne... |
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| SubjectTerms | 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 |
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| Title | Milne-type inequalities for third differentiable and h-convex functions |
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