Generalized Bullen Type Inequalities and Their Applications

Year 2025, Volume: 8 Issue: 2, 65 - 71, 30.06.2025

Mehmet Zeki Sarikaya

https://doi.org/10.33401/fujma.1557116

Abstract

This paper presents a novel extension of Bullen-type inequalities for convex functions by leveraging recently established generalized identities. Through rigorous proofs, we derive new inequalities that exhibit strong connections to both the left- and right-hand sides of the Hermite-Hadamard inequalities for Riemann-integrable functions. Additionally, we apply these results to various special means of two positive numbers.

Keywords

Convex function , Bullen inequality , Midpoint inequality , Trapezoid inequality , Hermite-Hadamard inequality

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