What question did this study set out to answer?

The aim is to explore the implications of the AM-GM inequality when applied to complex and mixed-sign pairs.

April 10, 2026Open Access

A Boundary Condition for the Arithmetic-Geometric Mean Inequality Under Complex Extension to Mixed-Sign Pairs

Key Points

The aim is to explore the implications of the AM-GM inequality when applied to complex and mixed-sign pairs.
Analyzed the classical AM-GM inequality framework.
Examined the effects of incorporating negative and mixed-sign numbers.
Developed mathematical proofs to investigate boundary conditions.
Identified specific conditions under which the AM-GM inequality holds for mixed-sign inputs.
Showed that certain pairs can violate the traditional AM-GM relationship.

Abstract

The classical AM-GM inequality states that for any two non-negative real numbers,the arithmetic mean is greater than or equal to the geometric mean. This paperinvestigates what happens when the inequality is extended to negative and mixed-signinputs.

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Mahmoud Bani Ata (Wed,) studied this question.

synapsesocial.com/papers/69d896566c1944d70ce07ac5 — DOI: https://doi.org/10.5281/zenodo.19474081

Authors

Mahmoud Bani Ata

Yarmouk University

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A Boundary Condition for the Arithmetic-Geometric Mean Inequality Under Complex Extension to Mixed-Sign Pairs

Key Points

Abstract

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Cite this study

Authors

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