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This paper considers a parametrized family of generalized Takagi functionsf_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 asimpler proof of this result by developing an explicit expression for f_p atdyadic rational points and showing that (1,p)-midconvexity of f_p reduces to asimple inequality for weighted sums of binary digits.

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