Doctoral thesis in Mathematics: Nonlinear metric regularity of set-valued mappings on a fixed set and applications

The dissertation has five chapters and a list of references. The chapters concentrate on the following issues: In Chapter 1, we recall some classical results of the problem and some basic concepts from variational analysis and nonsmooth analysis. In Chapter 2, we investigate some new models of nonlinear nonlocal regularity; Chapter 3 is devoted to the study of metric perturbation of Milyutin-type regularity on a fixed set under composition of a set-valued mapping and a Lipschitz single-valued mapping;...