• Communications of the Korean Mathematical Society
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• v.31 no.4
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• pp.811-817
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• 2016

Using the periodic continued fraction, we give concrete examples of the points at which the derivatives of the Minkowski question mark function does not exist. We also give examples of the differentiability points which show that recent apparently independent results are consistent and closely related.

• Journal of the Chungcheong Mathematical Society
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• v.22 no.2
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• pp.155-159
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• 2009

Using the Binet's formula, we show that the quotient related ratio $l_{1(x)}\;\neq\;0$ for the eventually periodic continued fraction x. Using this ratio, we also show that the derivative of the Minkowski question mark function at the simple periodic continued fraction is infinite or 0. In particular, $l_1({[\bar{1}]})$ = 2 log $\gamma$ where $\gamma$ is the golden mean $(1+\sqrt{5})/2$ and the derivative of the Minkowski question mark function at the simple periodic continued fraction $[\bar{1}]$ is infinite.