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Zbl 1127.49015
Ansari, Qamrul Hasan
Vectorial form of Ekeland-type variational principle with applications to vector equilibrium problems and fixed point theory. (English)
[J] J. Math. Anal. Appl. 334, No. 1, 561-575 (2007). ISSN 0022-247X

Summary: This paper introduces a vectorial form of equilibrium version of Ekeland-type variational principle. Some equivalent results to our variational principle are given. As applications, we derive the existence of solutions of a vector equilibrium problem in the setting of complete quasi-metric spaces with a $W$-distance. Caristi-Kirk fixed point theorem for multivalued maps is also established in a more general setting.

MSC 2000:: *49J53 Set-valued and variational analysis
49J27 Optimal control problems in abstract spaces (existence)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: vectorial form of Ekeland-type variational principle; vector equilibrium problems; complete quasi-metric spaces; Caristi-Kirk fixed point theorem

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