Stability and regular points of inequality systems
Journal of Optimization Theory and Applications
Metric regularity, openness and Lipschitzian behavior of multifunctions
Non-Linear Analysis
Variational pairs and applications to stability in nonsmooth analysis
Nonlinear Analysis: Theory, Methods & Applications
Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications (Nonconvex Optimization and Its Applications)
Towards variational analysis in metric spaces: metric regularity and fixed points
Mathematical Programming: Series A and B - Series B - Special Issue: Well-posedness, stability and related topics
Hölder metric regularity of set-valued maps
Mathematical Programming: Series A and B
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This paper is devoted to noninfinitesimal methods in nonlocal regularity theory for set-valued mappings between metric spaces and concentrates on studying two main interconnected topics: noninfinitesimal regularity criteria and fixed-points of set-valued mappings. A number of new results are proved, in particular those which cover and extend to a general metric setting some theorems viewed specifically as Banach-space results. In addition, a special technical interest in studying these two topics together is determined by the fact that each of them exploits a certain sequential iteration scheme (connected with Ekeland's principle in the first and Newton-type iterations in the second) and the extent to which each of the schemes can be effectively applied to the study of the other topic is at least unclear.