Decomposition of higher-order Wright convex functions revisited

Zsolt Páles; Mahmood Kamil Shihab

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arXiv · 2112.07387

Decomposition of higher-order Wright convex functions revisited

Zsolt Páles·Mahmood Kamil Shihab

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Abstract

In 2009, Maksa and P\'ales established an extension of the decomposition theorem of Ng in the context of higher-order convexity notions. They proved that a real function is Wright convex of order $n$ if and only if it can be decomposed as the sum of a convex function of order $n$ and a polynomial function of order at most $n$. Their proof was based on transfinite tools in the background. The main purpose of this paper is to adopt the methods of a paper of P\'ales published in 2020 and establish a new and elementary proof for the theorem of Maksa and P\'ales.

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Zsolt Páles, Mahmood Kamil Shihab. 2021-12-14. Decomposition of higher-order Wright convex functions revisited. https://arxiv.org/abs/2112.07387

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