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arXiv · 1009.1308

An inequality for sums of binary digits, with application to Takagi functions

Pieter C. Allaart
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Abstract

This paper considers a parametrized family of generalized Takagi functions f_p with parameter p. Tabor and Tabor [J. Math. Anal. Appl. 356 (2009), 729-737] recently proved that for p in [1,2], f_p is (1,p)-midconvex. We give a simpler proof of this result by developing an explicit expression for f_p at dyadic rational points and showing that (1,p)-midconvexity of f_p reduces to a simple inequality for weighted sums of binary digits.

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Pieter C. Allaart. 2010-09-07. An inequality for sums of binary digits, with application to Takagi functions. https://arxiv.org/abs/1009.1308

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