Vectorial form of Ekeland-type variational principle
Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok, 65000, Thailand
Fixed Point Theory and Applications 2012, 2012:127 doi:10.1186/1687-1812-2012-127Published: 2 August 2012
In this paper, we deal with a vectorial form of Ekeland-type variational principle for multivalued bioperator whose domain is a complete metric space and its range is a subset of a locally convex Hausdorff topological space. From this theorem, Caristi-Kirk fixed point theorem for multivalued maps is established in a more general setting and our techniques allow us to improve and to extend their results in (Ansari in J. Math. Anal. Appl. 335: 561-575, 2007; Bednarczuk and Zagrodny in Arch. Math. 93: 577-586, 2009; Bianchi, Kassay and Pini in J. Math. Anal. Appl. 305: 502-512, 2005).
MSC: 49K30, 90C29.