Some fixed point theorems for (α,θ,k)-contractive multi-valued mappings with some applications

In this paper, we introduce the notion of ( α , θ , k ) -contraction multi-valued mappings and establish some fixed point results for such mappings by using some control functions due to Jleli et al. (J. Inequal. Appl. 2014:439, 2014) in metric spaces and furnish some interesting examples to illustrate our main results. Also, we give some fixed point results in metric spaces endowed with a graph. Our results generalize and extend recent results given by some authors.