Abstract
This paper proposes a formally stronger set-valued Caristi's fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland's variational principle and this set-valued Caristi's fixed point theorem. The results stated in this paper improve and strengthen the corresponding results in [4].
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ekeland, I., On the variational principle,J. Math. Anal. Appl.,47 (1974), 324–353.
Ekeland, I., Nonconvex minimization problems,Bull. Amer. Math. Soc. (New Series),1 (1979), 443–474.
Caristi, J., Fixed point theorems for mappings satisfying inwardness conditions,Trans. Amer. Math. Soc.,215 (1976), 241–251.
Shi Shu-zhong, The equivalence between Ekeland's variational principle and Caristi's fixed point theorem,Advan. Math.,16, 2 (1987), 203–206. (in Chinese)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Shi-shen, Z., Qun, L. Set-valued Caristi's fixed point theorem and Ekfland's variational principle. Appl Math Mech 10, 119–121 (1989). https://doi.org/10.1007/BF02014818
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02014818