Azam et al. (Numer. Funct. Anal. Optim. 33(5):590-600, 2012) introduced the notion of complex-valued metric spaces and established a common fixed point result in the context of complex-valued metric spaces. In this paper, the existence of common fixed points is established for multi-valued mappings on the complex-valued metric spaces. Our results unify, generalize and complement the comparable results from the current literature. MSC:46S40, 47H10, 54H25.

In this paper, we introduce the notion of multivalued contractive mappings in complex valued metric space and prove common fixed point theorems for two multivalued contractive mappings in complex valued metric spaces without using the notion of continuity. Our results improve and extend the results of Azam et al. (2011).

In this article, we introduce Reich type contractions and ( )- contractions in the class of controlled metric spaces and establish some new related fixed point theorems. Our results are generalizations of some known results of literature. Some examples and certain consequences are given to illustrate significance of presented results.

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.

Using the concept of binary relation $R,$ we initiate a notion of ${\mathsf{\Theta }}_R$ -contraction and obtain some fixed point results for such mappings in the setting of complete metric spaces. Furthermore, we establish some new results of fixed points of N-order. Consequently, we improve and generalize the corresponding known fixed point results. As an application of our main result, we provide the existence of a solution for a class of nonlinear matrix equations. A numerical example is also presented to illustrate the theoretical findings.

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.