Some New Refinements of Jensen’s Discrete Inequality
DOI:
https://doi.org/10.5644/SJM.15.01.04Keywords:
Convex functions, Jensen’s inequality, Hermite-Hadamard’s inequalityAbstract
Some new refinements of the discrete Jensen's inequality are given. New upper and lower bounds for the discrete Jensen gap functional are discussed. These bounds are of two types. The first type is a hybrid of bounds given by several authors in different
works. The second type is appropriate for functions which are $r$-convex for some integer $r \ge 3$. A numerical example is presented. Some conjectures are made.
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