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This article is cited in 1 scientific paper (total in 1 paper)
Scientific articles
Existence of inverse function in a neighbourhood of a critical value
S. E. Zhukovskiyab, T. T. Ngoka a RUDN University
b V. A. Trapeznikov Institute of Control Sciences of RAS
Abstract:
The classical inverse function theorems guarantee the existence of an inverse function in a neighborhood of the value of a given point if the regularity condition is satisfied at this point, that is, the first derivative at a given point is nondegenerate. A more general condition for the existence of an implicit function is the 2-regularity condition. It holds, for example, for many quadratic mappings at zero. It is known that under natural smoothness assumptions, the existence of a continuous inverse function follows from a 2-regularity of a map at a point in a certain direction. In this paper, it is shown that, in the known statements guaranteeing the existence of an inverse function when the 2-regularity condition is satisfied, we can weaken the smoothness assumptions. However, the inverse function may not be continuous.
Keywords:
inverse function, 2 -regularity.
Received: 20.02.2019
Citation:
S. E. Zhukovskiy, T. T. Ngok, “Existence of inverse function in a neighbourhood of a critical value”, Russian Universities Reports. Mathematics, 24:126 (2019), 141–149
Linking options:
https://www.mathnet.ru/eng/vtamu142 https://www.mathnet.ru/eng/vtamu/v24/i126/p141
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Abstract page: | 88 | Full-text PDF : | 29 | References: | 24 |
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