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The main objective of this article is to consider the class of exponentially convex functions. We derive a new integral identity involving Riemann-Liouville fractional integral. Utilizing this identity as an auxiliary result we obtain new fractional bounds involving the functions having exponential convexity property. Publisher's Version

In this paper, we establish new renements and integral inequalities including concave functions. The reason why we choose the concave functions in this study is that the methods we use are applicable to these functions. Also some applications are provided.

The aim of the communication is to present the review of the Hermite-Hadamard inequality as the most important double inequality. We consider multivariate convex functions defined on simplices in the Euclidean space. The first thing we discuss is an extension of the Hermite-Hadamard inequality from the simplex barycenter to some other points. The second thing we are interested in is a two-sided refinement of this inequality. The third thing we want is to include the Fejér inequality in all of this. In the case of univariate convex functions, the Fejér inequality generalizes the Hermite-Hadamard inequality by using an additional symmetric function. Involving the concept of the barycenter of a positive integrable function, we can extend both inequalities.