On further refinements of the Jensen inequality and applications

We aim to extend some recent refinements of the Jensen inequality. First, we establish even more precise estimates for the Jensen inequality. Then, we derive an improvement of the Jensen inequality with regard to h$$ h $$‐convexity. As an application, our main results are applied in deriving refinem...

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Bibliographic Details
Published in:Mathematical methods in the applied sciences 2024-06, Vol.47 (9), p.7488-7501
Main Authors: Krnić, Mario, Minculete, Nicuşor, Mitroi‐Symeonidis, Flavia‐Corina
Format: Article
Language:English
Subjects:
Convexity
Estimates
f$$ f $$‐divergence
Information theory
Jensen inequality
power mean
refinement
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Summary:We aim to extend some recent refinements of the Jensen inequality. First, we establish even more precise estimates for the Jensen inequality. Then, we derive an improvement of the Jensen inequality with regard to h$$ h $$‐convexity. As an application, our main results are applied in deriving refinements of power mean inequalities and the Hölder inequality. Finally, we obtain more accurate estimates for f$$ f $$‐divergences, important in the information theory.
ISSN:0170-4214
1099-1476
DOI:10.1002/mma.9984