Some new fractional corrected Euler-Maclaurin type inequalities for function whose second derivatives are s-convex function

Abstract

Fractional integrals and inequalities have gained a lot of attention in recent years. By introducing innovative analytical approaches and applications, and by applying these approaches, numerous forms of inequalities have been examined. In this paper, we establish new identity for the twice differentiable function where the absolute value is convex. By utilizing this identity, numerous Corrected Euler-Maclaurin-type inequalities are developed for the Caputo-Fabrizio fractional integral operator. Based on this identity, the Corrected Euler-Maclaurin-type inequalities for [Formula: see text]-convex function are obtained. By employing well-known inequalities such as Hölder’s and Power -Mean, we are introduced several new error bounds and estimates for Corrected Euler-Maclaurin-type inequalities. Additionally, special cases of the present results are applied to obtain the previous well-known results.

Keywords

• Euler-Maclaurin-type inequalities
• -convex function
• fractional integrals
• corrected Euler-Maclaurin-type inequalities
• power-mean inequality