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
Hlavní autori:	Benaissa, Bouharket, Azzouz, Noureddine, Budak, Hüseyin
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	Cham Springer International Publishing 18.06.2024 Hindawi Limited SpringerOpen
Predmet:	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 Hermite–Hadamard inequality Fractional conformable integrals 26D10 Fractional conformable derivative 26D15 26A33
ISSN:	1687-2770, 1687-2762, 1687-2770
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Shrnutí:	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 .
Bibliografia:	ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14
ISSN:	1687-2770 1687-2762 1687-2770
DOI:	10.1186/s13661-024-01889-5