Abstract:
We consider smooth mappings acting from one Banach space to another and depending on a parameter belonging to a topological space. Under various regularity assumptions, sufficient conditions for the existence of global and semilocal continuous inverse and implicit functions are obtained. We consider applications of these results to the problem of continuous extension of implicit functions and to the problem of coincidence points of smooth and continuous compact mappings.
Keywords:global implicit function, implicit function extension, coincidence point.
UDC:517
Presented:A. B. Kurzhanski Received: 18.08.2020 Revised: 11.12.2020 Accepted: 12.12.2020