We introduce complex valued metric spaces and obtain sufficient conditions for the existence of common fixed points of a pair of mappings satisfying contractive type conditions.

In this article, inspired by the concepts of extended b-metric spaces, we introduce the notion of complex valued extended b-metric spaces. Using this new idea, some fixed point theorems involving rational contractive inequalities are proved. The established results herein augment several significant work in the comparable literature.

In this paper we extend the Banach contraction for multivalued mappings in a cone b-metric space without the assumption of normality on cones and generalize some attractive results in literature. MSC:47H10, 54H25.

In this paper we extend the Kannan, Chatterjea and Zamfirescu theorems for multivalued mappings in a tvs-cone metric space without the assumption of normality on cones and generalize many results in literature.

We introduce and study the notion of common coupled fixed points for a pair of mappings in complex valued metric space and demonstrate the existence and uniqueness of the common coupled fixed points in a complete complex-valued metric space in view of diverse contractive conditions. In addition, our investigations are well supported by nontrivial examples.