Some New Estimates for Integral Inequalities and Their Applications

We obtain several new integral inequalities in terms of fractional integral operators for the functions whose first derivatives satisfy either the conditions of the Lagrange theorem or the Lipschitz condition. In some special cases, the obtained results provide better upper estimates than the results known in the literature for the Bullen-type inequality and the Hadamard-type right-hand side inequality. Finally, some error estimates for the trapezoidal formula are discussed.