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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Bibliographic Details
Published in:Boundary value problems 2024-06, Vol.2024 (1), p.76-18
Main Authors: Benaissa, Bouharket, Azzouz, Noureddine, Budak, Hüseyin
Format: Article
Language:English
Subjects:
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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Summary: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 .
ISSN:1687-2762
1687-2770
DOI:10.1186/s13661-024-01889-5