On the Jensen functional and superquadraticity
Flavia-Corina Mitroi-Symeonidis, Nicu\c{s}or Minculete
TL;DR
This paper explores bounds for the Jensen functional under superquadraticity conditions, extending the analysis to Chebychev functionals and providing a generalized framework.
Contribution
It introduces a general approach to bounding Jensen functionals under superquadraticity and extends results to Chebychev functionals.
Findings
Derived bounds for Jensen functional under superquadraticity
Extended results to Chebychev functionals
Provided a generalized definition of these functionals
Abstract
In this note we give a recipe which describes upper and lower bounds for the Jensen functional under superquadraticity conditions. Some results involve the Chebychev functional. We give a more general definition of these functionals and establish the analogue results.
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