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 202424.png)
(
are Banach spaces with 203c205cinfty202424.png)
), 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.