ON GENERALIZATIONS OF INTEGRAL INEQUALITIES

Abstract

In the present study, several new generalized integral inequalities of the Hadamard and Simpson-type are obtained. The results were obtained for functions whose first and third derivatives are either convex or satisfy the Lipschitz condition or the conditions of the Lagrange theorem. In a particular case, these results not only confirm but also improve some upper bounds, well known in the literature for the Simpson and Hermite-Hadamard-type inequalities.

Keywords

• convex function
• hermite–hadamard inequality
• simpson-type inequality
• lipschitz conditions
• lagrange theorem
• riemann–liouville fractional integral