Weighted fractional inequalities for new conditions on h-convex functions
We use a new function class called B -function to establish a novel version of Hermite–Hadamard inequality for weighted ψ -Hilfer operators. Additionally, we prove two new identities involving weighted ψ -Hilfer operators for differentiable functions. Moreover, by employing these equalities and the...
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| Vydané v: | Boundary value problems Ročník 2024; číslo 1; s. 76 - 18 |
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| Hlavní autori: | , , |
| Médium: | Journal Article |
| Jazyk: | English |
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Springer International Publishing
18.06.2024
Hindawi Limited SpringerOpen |
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| ISSN: | 1687-2770, 1687-2762, 1687-2770 |
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| Abstract | We use a new function class called
B
-function to establish a novel version of Hermite–Hadamard inequality for weighted
ψ
-Hilfer operators. Additionally, we prove two new identities involving weighted
ψ
-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the
B
-function, we derive several trapezoid- and midpoint-type inequalities for
h
-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function
h
. |
|---|---|
| AbstractList | We use a new function class called
B
-function to establish a novel version of Hermite–Hadamard inequality for weighted
ψ
-Hilfer operators. Additionally, we prove two new identities involving weighted
ψ
-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the
B
-function, we derive several trapezoid- and midpoint-type inequalities for
h
-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function
h
. We use a new function class called B-function to establish a novel version of Hermite–Hadamard inequality for weighted ψ-Hilfer operators. Additionally, we prove two new identities involving weighted ψ-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B-function, we derive several trapezoid- and midpoint-type inequalities for h-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h. Abstract We use a new function class called B-function to establish a novel version of Hermite–Hadamard inequality for weighted ψ-Hilfer operators. Additionally, we prove two new identities involving weighted ψ-Hilfer operators for differentiable functions. Moreover, by employing these equalities and the properties of the B-function, we derive several trapezoid- and midpoint-type inequalities for h-convex functions. Furthermore, the obtained results are reduced to several well-known and some new inequalities by making specific choices of the function h. |
| ArticleNumber | 76 |
| Author | Azzouz, Noureddine Budak, Hüseyin Benaissa, Bouharket |
| Author_xml | – sequence: 1 givenname: Bouharket surname: Benaissa fullname: Benaissa, Bouharket organization: Laboratory of Informatics and Mathematics, Faculty of Material Sciences, University of Tiaret – sequence: 2 givenname: Noureddine surname: Azzouz fullname: Azzouz, Noureddine organization: Faculty of Sciences, University Center Nour Bachir, University Belhadj Bouchaib – sequence: 3 givenname: Hüseyin surname: Budak fullname: Budak, Hüseyin email: hsyn.budak@gmail.com organization: Department of Mathematics Faculty of Science and Arts, Düzce University |
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| Cites_doi | 10.1006/jmaa.1999.6593 10.18514/MMN.2023.4142 10.1016/j.jmaa.2006.02.086 10.1142/S0218348X20400113 10.1007/s13324-024-00893-3 10.22436/jnsa.009.03.50 10.18514/MMN.2017.1197 10.1016/j.mcm.2011.12.048 |
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| Snippet | We use a new function class called
B
-function to establish a novel version of Hermite–Hadamard inequality for weighted
ψ
-Hilfer operators. Additionally, we... We use a new function class called B-function to establish a novel version of Hermite–Hadamard inequality for weighted ψ-Hilfer operators. Additionally, we... Abstract We use a new function class called B-function to establish a novel version of Hermite–Hadamard inequality for weighted ψ-Hilfer operators.... |
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| SubjectTerms | Analysis Approximations and Expansions Boundary value problems Convex analysis Difference and Functional Equations Fractional conformable derivative Fractional conformable integrals Hermite–Hadamard inequality Identities Inequalities Integrals Mathematics Mathematics and Statistics Operators (mathematics) Ordinary Differential Equations Partial Differential Equations |
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| Title | Weighted fractional inequalities for new conditions on h-convex functions |
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