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

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

2010-09-07

arxiv.org/abs/1009.1308v3

J. Math. Anal. Appl. 381 (2), 689-694 (2011)

Mathematics

Classical Analysis and ODEs

11 pages, included more detail in the proofs and added a new Corollary 4

Scientific paper

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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