Well-Posedness and Porosity

Alexander J. Zaslavski ()
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Alexander J. Zaslavski: Technion - Israel Institute of Technology

Chapter 5 in Optimization on Metric and Normed Spaces, 2010, pp 181-224 from Springer

Abstract: Abstract 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 $$B_d (z,\alpha r) \subset B_d (y,r)\ \backslash\ E.$$

Keywords: Banach Space; Natural Number; Minimization Problem; Variational Principle; Equilibrium Problem (search for similar items in EconPapers)
Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-0-387-88621-3_5

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DOI: 10.1007/978-0-387-88621-3_5

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