Variational Analysis and Optimsiation Webinar, http://www.mocao.org/va-webinar/

Title: Continuous selections for inverse mappings in Banach spaces

Speaker: Radek Cibulka (University of West Bohemia)

Date and Time: October 28th, 2020, 17:00 AEDT (Register here for remote connection via Zoom)

Abstract: Influenced by a recent work by A. V. Arutyunov, A. F. Izmailov, and S. E. Zhukovskiy, we establish a general Ioffe-type criterion guaranteeing the existence of a continuous and calm selection for the inverse of a single-valued uniformly continuous mapping between Banach spaces with a closed domain. We show that the general statement yields elegant proofs following the same pattern as in the case of the usual openness with a linear rate by considering mappings instead of points. As in the case of the Ioffe’s criterion for linear openness around the reference point, this allows us to avoid the iteration, that is, the construction of a sequence of continuous functions the limit of which is the desired continuous selection for the inverse mapping, which is illustrated on the proof of the Bartle-Graves theorem. Then we formulate sufficient conditions based on approximations given by positively homogeneous mappings and bunches of linear operators. The talk is based on a joint work with Marián Fabian.

Author:	Vera Roshchina (via theBox)
Created:	29/10/2020
Updated:	28/10/2020
Theme:	Default
Copyright:	Creative Commons

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