A Refinement of the arithmetic-geometric mean inequality and some more
Mehdi Eghbali Amlashi, Mahmoud Hassani
TL;DR
This paper refines the classical AM-GM inequality and extends these improvements to Hilbert space inequalities, also providing refinements of the Kantorovich inequality, advancing mathematical bounds in analysis.
Contribution
It introduces a new refinement of the AM-GM inequality and applies it to Hilbert space inequalities, along with improved Kantorovich inequalities.
Findings
Refined the classical AM-GM inequality.
Extended the refinement to Hilbert space inequalities.
Provided improved bounds for Kantorovich inequality.
Abstract
In this note, we present a refinement of the well-known AM-GM inequality. We use this improved inequalty to establish corresponding inequalities on Hilbert space. We also give some refinements of the Kantorovich inequality.
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Taxonomy
TopicsMathematical Inequalities and Applications · Multi-Criteria Decision Making