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arXiv · 1901.06255

A note on $h$-convex functions

M. W. Alomari
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Abstract

In this work, we discuss the continuity of $h$-convex functions by introducing the concepts of $h$-convex curves ($h$-cord). Geometric interpretation of $h$-convexity is given. The fact that for a $h$-continuous function $f$, is being $h$-convex if and only if is $h$-midconvex is proved. Generally, we prove that if $f$ is $h$-convex then $f$ is $h$-continuous. A discussion regarding derivative characterization of $h$-convexity is also proposed.

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M. W. Alomari. 2019-01-07. A note on $h$-convex functions. https://arxiv.org/abs/1901.06255

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