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Öğe Bullen-Mercer type inequalities for the h-convex function with twice differentiable functions(Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, HuseyinBullen-type inequalities for h-convex functions using conformable fractional operators are established in this study on the cone of twice-differentiable functions. This is a novel fractional version of the existing Bullen-type inequalities with simple procedures using the B-function. Furthermore, new results on Bullen-type inequalities are presented for several specific cases of convexity, generalizing existing inequalities known in the literature.Öğe Hermite-Hadamard type inequalities for new conditions on h-convex functions via ? -Hilfer integral operators(Springer Basel Ag, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, HüseyinWe 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.Öğe Hermite-Hadamard-Mercer type inequalities for fractional integrals: A study with h-convexity and ψ-Hilfer operators(Springer, 2025) Azzouz, Noureddine; Benaissa, Bouharket; Budak, Hueseyin; Demir, IzzettinIn this paper, we first prove a generalized fractional version of Hermite-Hadamard-Mercer type inequalities using h-convex functions by means of psi-Hilfer fractional integral operators. Then, we give new identities of this type with special functions depending on psi. Moreover, we establish some new fractional integral inequalities connected with the right- and left-hand sides of Hermite-Hadamard-Mercer inequalities involving differentiable mappings whose absolute values of the derivatives are h-convex. For the development of these novel integral inequalities, we utilize h-Mercer inequality and H & ouml;lder's integral inequality. These results offer the significant advantage of being convertible into classical integral inequalities and Riemann-Liouville fractional integral inequalities for convex functions, s-convex functions, and P-convex functions.Öğe On generalized ψ-conformable calculus: Properties and inequalities(Univ Nis, Fac Sci Math, 2024) Azzouz, Noureddine; Benaissa, Bouharket; Budak, HuseyinIn this paper, we first introduce a new fractional derivatives and integrals called generalized psi-conformable derivative and generalized psi-conformable integral operators, respectively. We also show that these operators generalize various well-known fractional integral operators. Then, we present several properties of these operators including semi-group property. Moreover, we apply these operators to obtain a new Hermite-Hadamard-type inequality for convex functions. Furthermore, we obtain corresponding midpoint and trapezoid type inequalities for functions whose derivatives in absolute value are convex.Öğe On some Grüss-type inequalities via k-weighted fractional operators(Univ Nis, Fac Sci Math, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Sarıkaya, Mehmet ZekiIn 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.Öğe Simpson's quadrature formula for third differentiable and s-convex functions(Springer, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Sarikaya, Mehmet ZekiThis study establishes Newton-type inequalities for third differentiable and s-convex functions that use the Riemann integral. New Newton-type inequalities are also introduced using a summation parameter p >= 1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$p\geq 1$\end{document} for various convexity cases.Öğe Weighted fractional inequalities for new conditions on h-convex functions(Springer, 2024) Benaissa, Bouharket; Azzouz, Noureddine; Budak, HüseyinWe 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.
