DIFFERENTIABILITY AND NON-DIFFERENTIABILITY POINTS OF THE MINKOWSKI QUESTION MARK FUNCTION

Fractal Analysis for Sets of Non-differentiability of Minkowski’s Question Mark Function

In this paper we study various fractal geometric aspects in connection with Minkowski’s question mark function Q on the unit interval U . We show that U can be written as the union of the three sets Λ0 := {x : Q′(x) = 0} , Λ∞ := {x : Q′(x) = ∞} , and Λ∼ := {x : Q′(x) does not exist and Q′(x) 6= ∞}. The main result is that the Hausdorff dimensions of these sets are related as follows. dimH(νF) <...

Non-differentiability points of Cantor functions

Complex Function Differentiability

The articles [17], [18], [3], [5], [4], [8], [2], [7], [11], [6], [16], [12], [19], [9], [10], [1], [14], [15], and [13] provide the notation and terminology for this paper. For simplicity, we use the following convention: k, n, m denote elements of N, X denotes a set, s1, s2 denote complex sequences, Y denotes a subset of C, f , f1, f2 denote partial functions from C to C, r denotes a real num...

Fréchet directional differentiability and Fréchet differentiability

Zaj́ıček has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fréchet subdifferentiable but not Fréchet differentiable is first category. We introduce another variant of Fréchet differentiability, called Fréchet directional differentiability, and show that for any realvalued function on a normed linear space, the se...

On the Differentiability of the Policy Function∗

* The Research presented here started in August 1986 during our stay at the IMSSS, Stanford University; it was continued there during the Summer of 1987 and at the Insti-tuto de Analisis Economica, Universitat Autonoma de Barcelona in June-July 1988. We are very grateful to these institutions for their warm hospitality and support. Conversations with Manuel Santos and José Scheinkman were very ...