Approximate fixed point theorems for the generalized -set contraction mappings on an almost -space

In this paper, we use the conception of the abstract convexity to define the almost S - K K M C mapping, a l - S - K K M c ( X , Y , Z ) family, and almost Φ -spaces. In the setting of the almost Φ -spaces, we establish some new fixed point theorems for the a l - S - K K M c type set-valued mapping which is a generalized Ψ -set contraction mapping. Our results generalize the results of Amini et al. (2007) [4].