Generalizations of Euler-Maclaurin-Type Inequalities for Fractional Integrals with Respect to Another Function

Abstract

In this study, we provide a new perspective on differentiable convex functions by employing fractional integrals with respect to another function. Within this study, we establish new Euler-Maclaurin-type inequalities associated with these fractional integral operators. The proofs are based on fundamental mathematical tools, including convexity, Holder's inequality, and the power-mean inequality. Furthermore, we derive new inequalities for functions with bounded derivatives and for Lipschitz functions. Under appropriate parameter choices, the obtained results reduce to several well-known inequalities previously established in the literature.

Keywords

• Quadrature formula
• Maclaurin's formula
• fractional integrals
• bounded functions

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