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

Ansari, Q.H. and Sharma, P.K. (2019) Ekeland type variational principle for set-valued maps in quasi-metric spaces with applications. Journal of Nonlinear and Convex Analysis, 20 (8), 1683-1700.

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Abstract

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.

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Published date: October 2019

Additional Information: Funding Information: In this paper, first author was supported by DST-SERB Project No. MTR/2017/000135.

Keywords: Ekeland type variational principle, Fixed point theorem, Generalized variable order relations, Minimal element theorems, Set-valued maps, Variational rationality