کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6417657 | 1339300 | 2016 | 28 صفحه PDF | دانلود رایگان |
We consider a one-parameter family of functions {F(t,x)}t on [0,1] and partial derivatives âtkF(t,x) with respect to the parameter t. Each function of the class is defined by a certain pair of two square matrices of order two. The class includes the Lebesgue singular functions and other singular functions. Our approach to the Takagi function is similar to Hata and Yamaguti. The class of partial derivatives âtkF(t,x) includes the original Takagi function and some generalizations. We consider real-analytic properties of âtkF(t,x) as a function of x, specifically, differentiability, the Hausdorff dimension of the graph, the asymptotics around dyadic rationals, variation, a question of local monotonicity and a local modulus of continuity. Our results are extensions of some results for the original Takagi function and some generalizations.
Journal: Journal of Mathematical Analysis and Applications - Volume 434, Issue 1, 1 February 2016, Pages 652-679