Abstract:In this paper, we present several new and generalized Hermite-Hadamard type inequalities for s-convex as well as s-concave functions via classical and Riemann-Liouville fractional integrals. As applications, we provide new error estimations for the trapezoidal formula.

In this paper, we give generalizations of Jensen's, Jensen-Steffensen's and converse of Jensen's inequalities by using generalized majorization inequalities. We also present Grüss and Ostrowski-type inequalities for the generalized inequalities.

Abstract. In this paper, we use generalized majorization theorem and give the generalizations of Jensen's and Jensen-Steffensen's inequalities. We present the generalization of converse of Jensen's inequality. We give bounds for the identities related to the generalization of Jensen's inequality by usingČebyšev functionals. We also give Grüss and Ostrowski types inequalities for these functionals. We present mean value theorems and n -exponential convexity which leads to exponential convexity and log -convexity for these functionals. We give some families of functions which enable us to construct a large families of functions that are exponentially convex and also give classes of means.Mathematics subject classification (2010): 26D15.

In this paper, we give Hermite–Hadamard type inequalities of the Jensen–Mercer type for Riemann–Liouville fractional integrals. We prove integral identities, and with the help of these identities and some other eminent inequalities, such as Jensen, Hölder, and power mean inequalities, we obtain bounds for the difference of the newly obtained inequalities.