ON FIXED POINTS OF GENERALIZED SET-VALUED CONTRACTIONS

S. BENAHMED, D. AZÉ
2009 Bulletin of the Australian Mathematical Society  
Using a variational method introduced in [D. Azé and J.-N. Corvellec, 'A variational method in fixed point results with inwardness conditions', Proc. Amer. Math. Soc. 134(12) (2006), 3577-3583], deriving directly from the Ekeland principle, we give a general result on the existence of a fixed point for a very general class of multifunctions, generalizing the recent results of [Y. Feng and S. Liu, 'Fixed point theorems for multi-valued contractive mappings and multi-valued Caristi type
more » ... isti type mappings', J. Math. Anal. Appl. 317(1) (2006), 103-112; D. Klim and D. Wardowski, 'Fixed point theorems for set-valued contractions in complete metric spaces', J. Math. Anal. Appl. 334(1) (2007), 132-139]. Moreover, we give a sharp estimate for the distance to the fixed-points set. 2000 Mathematics subject classification: primary 54H25, 47H10.
doi:10.1017/s000497270900046x fatcat:47p6gijc6vdt7fht74n57wciiq