Extending the Scope of the Nesbitt Inequality: A Parametric and Functional Approach

Abstract

This paper makes three main contributions to the study of the Nesbitt inequality. First, we revisit a three-variable parametric extension and present a more transparent proof of a known result. Second, building on this proof, we generalize the inequality to the multivariable setting and identify acceptable parameter constraints. Third, we further broaden this framework using convex and increasing functions. Finally, we formulate an open problem regarding the necessary and sufficient conditions on the involved parameters.