TL;DR
This paper establishes optimal inequalities for bounded functions based on their deviation from the mean, extending previous results by Thong and Perfetti to provide more general bounds.
Contribution
It introduces generalized and optimal inequalities for bounded functions' deviations from their mean, expanding upon prior specific cases.
Findings
Derived new bounds for bounded functions
Extended known inequalities to more general cases
Provided optimal constants in the inequalities
Abstract
In this note we prove optimal inequalities for bounded functions in terms of their deviation from their mean. These results extend and generalize some known inequalities due to Thong (2011) and Perfetti (2011)
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