度量正则映射的一个反函数定理
An Inverse Function Theorem for Metrically Regular Mappings
摘要：
本文证明了：如果一个映射F：X到Y，其中X和Y是巴拿赫空间，且它的逆函数F^{-1}是凸的且在（x，y）周围局部闭值，则对任何函数G：X到Y，且有唇G（x）regF（x| y））< 1时，映射（F+G）^{-1}在（x，y+G（x））周围具有连续的局部选择，这也是平静的。
英文摘要：
We prove that if a mapping F:X to Y, where X and Y are Banach spaces, is metrically regular at x for y and its inverse F^{-1} is convex and closed valued locally around (x,y), then for any function G:X to Y with lip G(x)regF(x|y)) < 1, the mapping (F+G)^{-1} has a continuous local selection around (x, y+G(x)) which is also calm.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
