Frechet vs. Gateaux Differentiability of Lipschitzian Functions
Copyright policy )Frechet vs. Gateaux Differentiability of Lipschitzian Functions
Examples have been given of Lipschitzian functions that are Gâteaux-differentiable everywhere, but nowhere Fréchet-differentiable. One such example has been reported, mistakenly, in several papers as having domain in L 2 ( [ 0 , π ] ) {L^2}([0,\pi ]) , when it should have been L 1 ( [ 0 , π ] ) {L^1}([0,\pi ]) . We discuss this example.
- University of Kansas United States
Calculus of functions on infinite-dimensional spaces, Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives, Gâteaux differentiable, Lipschitzian function, Fréchet differentiable, Fréchet and Gateaux differentiability in optimization
Calculus of functions on infinite-dimensional spaces, Nondifferentiability (nondifferentiable functions, points of nondifferentiability), discontinuous derivatives, Gâteaux differentiable, Lipschitzian function, Fréchet differentiable, Fréchet and Gateaux differentiability in optimization
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