New areas of fixed point results for multi-valued mappings and its applications

Banach’s contraction has been generalized in several approaches by many scholars [1, 2, 3, 4, 10, 13]. In 2012, Sedghi et al. generalized metric space called S-metric space (S-ms) [12, 5, 6]. This study, investigate some new common fixed point results for single-valued and multi-valued mappings are proven in S-ms by using a generalization of coincidence point for pair (f, F), in which f is single-valued and F is a multi-valued mapping. Also we generalized the concepts in [8] on an S-ms accomplished with a finite number of graphs and present an application and an example. In this note, (X, S) is an S-ms and G = {Gα : α = 1, 2..., l} is the set of all graphs where Gα = (X, Eα), Eα ⊆ X × X × X for each α ∈ {1, 2, ..., l}.