Coincidence point results for hybrid pair of mappings on a dislocated metric space endowed with an arbitrary binary relation

Abstract

We introduce the notion of generalized S-contraction of Nadler type and prove some new coincidence point results for hybrid pair of mappings in 0-complete dislocated metric spaces endowed with an arbitrary binary relation. Our results generalize, extend and unify several well known comparable results including Nadler’s fixed point theorem in the setting of dislocated metric spaces. As some applications of our main result, we can obtain several important fixed point results of multi-valued mappings satisfying some contractive type conditions of Kannan type, Fisher type etc. in this new framework. Moreover, we provide some examples to justify that the generalization is proper.