Well-Posedness and Porosity

Part of the Springer Optimization and Its Applications book series (SOIA, volume 44)


We recall the concept of porosity [10, 26, 27, 84, 97, 98, 112]. Let (Y, d) be a complete metric space. We denote by Bd(y, r) the closed ball of center \(y\ \in\ Y,\) and radius r > 0. A subset \(E \subset Y\) is called porous with respect to d (or just porous if the metric is understood) if there exist \(\alpha \in\) (0, 1] and r0 > 0 such that for each \(r \in\) (0, r0] and each \(y \in Y\) there exists \(z \in Y\) for which \(B_d (z,\alpha r) \subset B_d (y,r)\ \backslash\ E.\)


Banach Space Natural Number Minimization Problem Variational Principle Equilibrium Problem 
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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of MathematicsTechnion - Israel Institute of TechnologyHaifaIsrael

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