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On a domain of invertibility of a differentiable mapping
Abstract
This paper deals with a domain and its range of
invertibility of a differentiable mapping at a point with an invertible
derivative. Assuming the C2-class
of a mapping T defined in a neighbourhood of a point x0 in Banach space
with
an invertible derivative, we look for estimations of radii of balls with
centers in x0 and T (x0)
which are contained in a domain of invertibility of T and its range,
respectively.
Mathematics Subject
Classification (2000): 47J07, 35J30, 34B15
Quaestiones Mathematicae 25 (2002), 163-170
invertibility of a differentiable mapping at a point with an invertible
derivative. Assuming the C2-class
of a mapping T defined in a neighbourhood of a point x0 in Banach space
with
an invertible derivative, we look for estimations of radii of balls with
centers in x0 and T (x0)
which are contained in a domain of invertibility of T and its range,
respectively.
Mathematics Subject
Classification (2000): 47J07, 35J30, 34B15
Quaestiones Mathematicae 25 (2002), 163-170
