In this paper, we establish a new auxiliary identity of the Bullen type for twice-differentiable functions in terms of fractional integral operators. Based on this new identity, some generalized Bullen-type inequalities are obtained by employing convexity properties. Concrete examples are given to illustrate the results, and the correctness is confirmed by graphical analysis. An analysis is provided on the estimations of bounds. According to calculations, improved Hölder and power mean inequalities give better upper-bound results than classical inequalities. Lastly, some applications to quadrature rules, modified Bessel functions and digamma functions are provided as well.

In this paper, we establish several new integral inequalities for (α, s, m)-convex functions. We recapture the Hermite-Hadamard inequality as a particular case. In order to obtain our results, we use classical inequalities such as Hölder inequality, Hölder-Işcan inequality and Power mean inequality. We formulate several bounds involving special functions like classical Euler-Gamma, Beta and PsiGamma functions. We also give some applications.

In this paper, we establish new Hermite-Hadamard inequalities for h-convex functions, with in the framework of a previously defined generalized integral. The results obtained, generalize or complete, several reported in the literature. Some final remarks show the strength and scope of our results.

In this article, we establish several inequalities for $(h,m)$-convex maps, related to weighted integrals, used in previous works. Throughout the work, we show that our results generalize several of the integral inequalities known from the literature.

In this paper, using the definition of functions (h,m,s)-convex modified of second type, various extensions of the classic Hermite-Hadamard Inequality are obtained using Katugampola integrals. In addition, we show that several results known are particular cases of ours.