Fixed Point Theorems for Multi-valued Contractions by Altering Distance in Complete Metric Spaces

In the present paper, the concept of generalized contractions for set-valued maps in metric spaces is introduced and the existence of fixed point for such a contraction are guaranteed by certain conditions. Presented results generalize and improve the recent results of Ciric, Y. Feng-S. Liu, Klim-Wardowski and several others. The method used in the proofs of our results is inspired by Ciric idea. Comparisons and examples are given.