Abstract
Functions \({f\colon D\rightarrow \mathbb{R}}\) defined on an open convex subset of \({\mathbb{R}^n}\) satisfying the approximate type convexity condition with bound of the form \({\varepsilon \sqrt{t(1-t)} \|x-y\|}\) are considered. We discuss properties concerning such functions characteristic for convex functions.
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The paper is dedicated to Professor János Aczél on the occasion of his 90th birthday
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Żołdak, M. Approximate convexity with the standard deviation’s error. Aequat. Math. 89, 449–457 (2015). https://doi.org/10.1007/s00010-015-0348-0
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DOI: https://doi.org/10.1007/s00010-015-0348-0