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2015-12-08 Nonlinear Seminar

Mateusz Krukowski
Darbo type theorem for quasi-measures of non-compactness.

This presentation introduces the notion of a quasi-measure of non-compactness. Such functions need not to be invariant in a convex hull in contrast to classical measures of non-compactness. Using the compactness criterion in the space $$ BC(X,E) $$ ($$ X, E $$ are Banach spaces with $$ \dim(X) < \infty $$), we construct a quasi-measure of non-compactness and study its properties. Furthermore we prove the analog of the Darbo theorem using the measure of non-convexity. We also show the application of the shown tools to finding a fixed point of the Hammerstein operator.