Abstract

We prove that the function ξ∈RN→∣ξ∣p\xi\in \mathbb{R}^N\rightarrow \vert \xi\vert^p is strongly convex for every pp, p∈]1,+∞[p\in]1,+\infty[, and we give a characterization, through the resolution of an algebraic equation, of the best constant which appears in the strong convexity inequality. The same proof allows us to prove that the function ξ∈RN→∣ξ∣p−2ξ\xi\in \mathbb{R}^N\to \vert \xi\vert^{p-2}\xi is strongly monotone and to identify the explicit value of the best constant.

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Keywords

  • Strong convexity
  • strong monotonicity
  • best constants

Mathematics Subject Classification

26B25

References

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Suggested citation

A. Gaudiello, O. Guibé, F. Murat. “The Best Constants in the Strong Convexity of |ξ|^p and in the Strong Monotonicity of |ξ|^{p-2}ξ.” Journal of Convex Analysis 33 (2026), No. 3&4, 875–902. https://doi.org/10.68381/jca33049

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Published by Heldermann Verlag, 2026. Rights now held by Banach Press LLC.