Ekeland type variational principle for set-valued maps in quasi-metric spaces with applications

In this paper, we derive a fixed point theorem, minimal element theorems and Ekeland type variational principle for set-valued maps with generalized variable set relations in quasi-metric spaces. These generalized variable set relations are the generalizations of set relations with constant ordering cone, and form the modern approach to compare sets in set-valued optimization with respect to variable domination structures under some appropriate assumptions. At the end, we give application of these variational principles to the capability theory of well-beings via variational rationality.