Common Fixed Point Theorems of Generalized Multivalued (ψ,ϕ)-Contractions in Complete Metric Spaces with Application

The purpose of this paper is to introduce the notion of generalized multivalued ψ , ϕ-type contractions and generalized multivalued ψ , ϕ-type Suzuki contractions and establish some new common fixed point theorems for such multivalued mappings in complete metric spaces. Our results are extension and improvement of the Suzuki and Nadler contraction theorems, Jleli and Samet, Piri and Kumam, Mizoguchi and Takahashi, and Liu et al. fixed point theorems. We provide an example for supporting our new results. Moreover, an application of our main result to the existence of solution of system of functional equations is also presented.