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}.