Covering and Metric Regularity
Alexandru V. Blaga, Mihai Eminescu, Alexandru V. Blaga · 2009
Abstract. We consider some theorems on the covering property of map-pings defined between Banach spaces. Also we study some related properties and propose nonlocal theorems of the covering-type or contract. It is known that the covering property and metric regularity property are equivalent. The author’s opinion is that among these two properties, the more convenient for applications, for usage in concrete situations is metric regularity (the distance estimate to the level sets), whereas the more convenient to prove is covering.