Generalized Bullen Type Inequalities and Their Applications

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

References

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