1,811 research outputs found
G\^ ateaux and Hadamard differentiability via directional differentiability
Let be a separable Banach space, a Banach space and an
arbitrary mapping. Then the following implication holds at each point
except a -directionally porous set:
If the one-sided Hadamard directional derivative exists in all
directions from a set whose linear span is dense in ,
then is Hadamard differentiable at .
This theorem improves and generalizes a recent result of A.D. Ioffe, in which
the linear span of equals and .
An analogous theorem, in which is pointwise Lipschitz, and which deals
with the usual one-sided derivatives and G\^ ateaux differentiability is also
proved. It generalizes a result of D. Preiss and the author, in which is
supposed to be Lipschitz
Properties of Hadamard directional derivatives: Denjoy-Young-Saks theorem for functions on Banach spaces
The classical Denjoy-Young-Saks theorem on Dini derivatives of arbitrary
functions was extended by U.S. Haslam-Jones (1932) and A.J. Ward
(1935) to arbitrary functions on . This extension gives the strongest
relation among upper and lower Hadamard directional derivatives ,
() which holds almost everywhere for an arbitrary
function . Our main result extends the theorem of Haslam-Jones
and Ward to functions on separable Banach spaces
Around the Fed: Safety first?
Related link(s): http://www.richmondfed.org/publications/research/region_focus/2009/summer/around_the_fed_weblinks.cfmEconomics
Curves in Banach spaces which allow a parametrization
We give a complete characterization of those (where is a
Banach space which admits an equivalent Fr\'echet smooth norm) which allow an
equivalent parametrization. For , a characterization is well-known.
However, even in the case , several quite new ideas are needed.
Moreover, the very close case of parametrizations with a bounded second
derivative is solved.Comment: 22 pages; We split the original paper into two parts. This is the
first part ( paths), the second part (paths with finite convexity) will
appear late
Advancing immunity : what is the role for policy in the private decision to vaccinate children?
Related links: http://www.richmondfed.org/publications/research/region_focus/2010/q2/feature2_weblinks.cfmPublic health - Economic aspects
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