In this article, we present an identity and several Hermite-Hadamard type inequalities for conformable fractional integrals. As applications, we establish some inequalities for certain special means of two positive real numbers and give the error estimations for the trapezoidal formula.

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In this paper, we discover two novel integral identities for twice differentiable functions. Under the utility of these identities, we establish some generalized inequalities for classical integrals and Riemann-Liouville fractional integrals of the Hermite-Hadamard type via functions whose derivatives absolute values are MTconvex. At the end, we present applications for special means and several error approximations for the trapezoidal formula.

Abstract. In this article first, we give an integral identity and prove some Hermite-Hadamard type inequalities for the function f such that |f | q is convex or concave for q ≥ 1. Second, by using these results, we present applications to f -divergence measures. At the end, we obtain some bounds for special means of real numbers and new error estimates for the trapezoidal formula.

In this paper our aim is to give refinements of Jensen's type inequalities for the convex function defined on the coordinates of the bidimensional interval in the plane.