BUILD AN INVERSE FUNCTION IN A NEIGHBOURHOOD OF AN ABNORMAL POINT UNDER WEAK SMOOTHNESS ASSUMPTIONS
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Abstract
Inverse mapping has been studied and used extensively in mathematics. Especially, it is also widely accepted in information technology and electromagnetic devices. This article studies an existence of an inverse mapping function in the neighbourhood of a degenerate point under weak smoothness assumptions. Initially, a continuous map x is regarded at the degenerate point, specifically at zero points, when the first derivative is zero and exists the second derivative with an assumption that the map has weakened smoothness. We then prove that there exists an inverse mapping. From there, we develop and prove the existence of an inverse mapping when the first derivative at a given degenerate point with the weak smoothness of that mapping.
Keywords
Brouwer, degenerate point, inverse function, inverse mapping, quadratic map, reverse mapping, weak smoothness
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References
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