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operator norm

Defines: 
bounded linear map, unbounded linear map, bounded operator, unbounded operator
Synonym: 
induced norm
Type of Math Object: 
Definition
Major Section: 
Reference

Mathematics Subject Classification

47L25 no label found46A32 no label found47A30 no label found

Comments

I faced a problem:
f:U-->R is uniformly partiallly differentiaable at a , i.e.,
for any epsilon, there exists a delta so that:
|[f(a+tu)-f(a)]/t-Dfu(a)|<=epsilon
for all u belongs to Rn and ||u||=1 and all t with 0<|t|<delta.

show that f is diffentiable at a

*Dfu(a) is the patial dirivative of f in the direction of u.

I got a proof but I am not confident in it because this kind of basic concept problem need to be very accurate..but I am quite confused about some symbol and concept .

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