In this paper we introduce vector metric spaces and we give some properties of this spaces. Also we prove Baire theorem and Banach fixed point theorem on this spaces.

In this paper we give some theorems on point of coincidence and common fixed points for two self mappings satisfying some general contractive conditions in vector metric spaces. Our results generalize some well-known recent results.

In this paper, considering an order relation on a vector metric space which is introduced by Ç evik and Altun in 2009, we present some fundamental fixed point results. Then, we provide some nontrivial examples show that the investigation of this work is significant.

We introduce vectorial and topological continuities for functions defined on vector metric spaces and illustrate spaces of such functions. Also, we describe some fundamental classes of vector valued functions and extension theorems.

In this paper, we define ordered vectorial quasi contractions. We show that ordered quasi contractions are ordered vectorial quasi contractions, but the reverse is not true. We also define ordered vectorial almost contractions and present fixed point theorems for this type of contractions. Hence, we disclose many results in the literature. With the help of examples, we illustrate the relationship between these two types of contractions and some others in the literature.