Abstract :
In this paper the concept of a contraction for multi-valued mappings in a metric space is
introduced and the existence theorems for fixed points of such contractions in a complete
metric space are proved. Presented results generalize and improve the recent results of
Y. Feng, S. Liu [Y. Feng, S. Liu, Fixed point theorems for multi-valued contractive mappings
and multi-valued Caristi type mappings, J. Math. Anal. Appl. 317 (2006) 103–112], D. Klim,
D. Wardowski [D. Klim, D. Wardowski, Fixed point theorems for set-valued contractions
in complete metric spaces, J. Math. Anal. Appl. 334 (2007) 132–139] and several others.
The method used in the proofs of our results is new and is simpler than methods used in
the corresponding papers. Two examples are given to show that our results are genuine
generalization of the results of Feng and Liu and Klim and Wardowski
