Reversibility of the inverse function theorem for differentiable functions
1 Department of Higher Mathematics, National University of Water and Environmental Engineering, Rivne, 33028, Ukraine
Keywords:
inverse function, differentiable function
Abstract
Let
X
and
Y
be Banach spaces,
U
⊂
X
be an open set and
k
∈
N
∪{∞}
. It is shown that a
C
k
-mapping
F
:
U
→
Y
is a local
C
k
-diffeomorphism at a point
x
0
∈
U
if and only if the derivative
of
(
DF
)
x
0
:
X
→
Y
is a linear isomorphism.
Cite
- ACS Style
- Slyusarchuk , V.Y. Reversibility of the inverse function theorem for differentiable functions. Bukovinian Mathematical Journal. 2016, 2
- AMA Style
- Slyusarchuk VY. Reversibility of the inverse function theorem for differentiable functions. Bukovinian Mathematical Journal. 2016; 2(4).
- Chicago/Turabian Style
- Vasyl Yukhimovych Slyusarchuk . 2016. "Reversibility of the inverse function theorem for differentiable functions". Bukovinian Mathematical Journal. 2 no. 4.
Export