Corrected Euler-Maclaurin Type Inequalities for Differentiable $s$-Convex Functions

Year 2025, Volume: 13 Issue: 1, 37 - 49, 30.04.2025

Saliha Djenaoui , Badreddine Meftah

Abstract

Integral inequalities are generally applicable in many branches of mathematics such as real, complex, and numerical analysis, as well as in other disciplines outside mathematics. In this work, we first prove a new identity. Based on this equality, we establish some new corrected Euler-Maclaurin type inequalities for functions whose first derivatives are $% s$-convex. The case where the first derivative is bounded as well as Lipschitzians are also discussed. Some applications to quadrature formulas and inequalities involving means are provided.

Keywords

s convex functions, Lipschtizian functions, bounded functions, correction Euler Maclaurin inequality

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