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Comprehensive analysis reveals enhanced outcomes of Hermite-Hadamard inequalities in optimization theory, suggesting improved methodologies.
In this article, we explore a novel class of Hermite-Hadamard inequalities via exponential type convexity. To establish the main results, we primarily use H?lder?s inequality, the power mean inequality and some generalized associated inequalities. These inequalities have strong applicability in inequalities and optimization theory. Moreover, we compare the main findings to demonstrate that the H?lder-??an inequality can yield more refined results than H?lder?s inequality and the improved power mean inequality can offer better refinements of Hermite-Hadamard inequalities than the power mean inequality. Additionally, we provide some applications for generalized means.
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Samraiz et al. (2025) studied this question.
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