Mathematical analysis demonstrates refined Hermite-Hadamard inequalities with improved bounds for uniformly convex functions, suggesting enhanced precision in evaluating special means.
In this paper a new Hermite-Hadamard-type inequality for uniformly convex functions is established and several consequences from it in connection with the integral mean are derived. Then a refined version of Hermite-Hadamard-type inequality for uniformly convex functions with both, the upper and lower bounds improved is presented. In addition, several applications to special means are presented. Some examples and graphics will be given and will validate the obtained results by using the software MATLAB R2023b.
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Mirzadeh et al. (2026) studied this question.
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