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In this article, we aim to establish several inequalities for differentiable exponentially convex and exponentially quasi-convex mapping, which are connected with the famous Hermite–Hadamard (HH) integral inequality. Moreover, we have provided applications of our findings to error estimations in numerical analysis and higher moments of random variables.

On Some New Weighted Inequalities for Differentiable Exponentially Convex and Exponentially Quasi-Convex Functions with Applications