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

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