Abstract:Zaj\'\i{}\v{c}ek has recently shown that for a lower semi-continuous real-valued function on an Asplund space, the set of points where the function is Fr\'echet subdifferentiable but not Fr\'echet differentiable is first category. We introduce another variant of Fr\'echet differentiability, called Fr\'echet directional differentiability, and show that for any real-valued function on a normed linear space, the set of points where the function is Fr\'echet directionally differentiable but not Fr\'echet differentiable is first category.
Keywords: G\^ateaux and Fr\'echet subdifferentiability, directional differentiability, strict and intermediate differentiability
AMS Subject Classification: 58C20, 46G05