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    Hermite-Hadamard type inequalities for new conditions on h-convex functions via ? -Hilfer integral operators
    (Springer Basel Ag, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, Hüseyin
    We employ a new function class called B-function to create a new version of fractional Hermite-Hadamard and trapezoid type inequalities on the right-hand side that involves h-convex and psi -Hilfer operators. We also provide new midpoint-type inequalities using h-convex functions.
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    On some Grüss-type inequalities via k-weighted fractional operators
    (Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Sarıkaya, Mehmet Zeki
    In this paper, we employ the concept of k-weighted fractional integration of one function with respect to another function to extend the scope of Gr & uuml;ss-type fractional integral inequalities. Furthermore, we establish and provide proofs for a set of inequalities that incorporate k-weighted fractional integrals.
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    Weighted fractional inequalities for new conditions on h-convex functions
    (Springer, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, Hüseyin
    We use a new function class called B-function to establish a novel version of Hermite-Hadamard inequality for weighted psi-Hilfer operators. Additionally, we prove two new identities involving weighted psi-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.