2023•Annals of the University of Craiova Mathematics and Computer Science SeriesOpen access

On convex functions and related inequalities

Parvaneh Vaziri, Hadi Khodabakhshian, Rahim Safshekan

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Abstract

The main result of this paper is to give refinement and reverse the celebrated Jensen inequality. We directly apply our results to establish several weighted arithmetic-geometric mean inequality. We also present a stronger estimate for the first inequality in the Hermite-Hadamard inequality.

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What this paper is about

The main result of this paper is to give refinement and reverse the celebrated Jensen inequality. We directly apply our results to establish several weighted arithmetic-geometric mean inequality. We also present a stronger estimate for the first inequality in the Hermite-Hadamard inequality.

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Available abstract

The main result of this paper is to give refinement and reverse the celebrated Jensen inequality. We directly apply our results to establish several weighted arithmetic-geometric mean inequality. We also present a stronger estimate for the first inequality in the Hermite-Hadamard inequality.

Key concepts: Mathematics, Inequality of arithmetic and geometric means, Inequality, Jensen's inequality, Convex function, Regular polygon, Young's inequality, Hermite polynomials

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