Integral inequalities and their applications

This thesis consists of two main parts. In the first part, new Hermite-Hadamard inequalities for h-convex functions are obtained and the applications of obtained results to some special means are provided. Besides that, new Hermite-Hadamard-Mercer type inequalities involving Riemann-Liouville fractional integrals for convex functions are proved, and their applications to some special means are got. In the second part, a new kind of convexity called (p,φh)-convexity is defined and its properties are established. Then, new Hermite-Hadamard,Hermite-Hadamard-Fejér, Ostrowski, Jensen and Jensen-Mercer types inequalities for (p,φh)-convex functions are proved. Finally, new Hermite-Hadamard type inequalities for (p,φh)-convex functions via Riemann-Liouville fractional integrals are obtained.