In this paper, we consider E-b-metric space, which is a generalized vector metric space.The metric is Riesz space valued. Here, we prove some results concerning common fixed point for four mappings on E-b-metric spaces. This generalizes the results of Rahimi, Abbas and Rad [4 ]. Keyword-E-b-metric space, Riesz space, weak annihilators, weakly compatible, weakly increasing I. INTRODUCTION Rahimi, Abbas and Rad [15] established few common fixed point results on ordered vector metric spaces for four mappings. Motivated by their work, we extend some of their results of common fixed point theorems for operators defined on Ebmetric space. Altun and Cevik([7],[8]) have proved some results for vector metric space, which is Riesz space valued metric space. Ebmetric space was defined by Petre [13]. He combined the notions of vector metric space and bmetric space. We recall the basic concepts and notations introduced by Altun and Cevik ([4],[6]) and Petre [13]. We follow notions and terminology by Aliprantis and Border [3] and Luxemburg and Zannen [11] for Riesz spaces. Definition 1.1. A partial order is a binary relation on a set X which is reflexive, antisymmetric and transitive .A set with partial order is called a partially ordered set. A partially ordered set (X, ) is said to be linearly ordered or totally ordered or a chain if for each pair x, y X, we have either x y or y x. A partially ordered set in which every two elements has a supremum or an infimum is called a lattice.A lattice in X is said to be complete if every subset has supremum or an infimum and Dedikind complete if every nonempty subset which is bounded above (below), has a supremum (infimum). A sequence (b n) is said to be order Cauchy (oCauchy) if there exists a sequence (a n) in E such that a n 0 and |b n b n+p | ≤ a n holds for n and p. Definition 1.2. A real vector space equipped with partial order vector space (E, ≤) is said to be partially ordered vector space if for x, y, z E and α 0, (i) x y implies x + z y + z. (ii) x y impies αx αy. Definition1,3. A partially ordered vector space which is also a lattice under its ordering, is called a Riesz space. Notation: If (x n) is a decreasing sequence in a Riesz space E such that g.l.b. x n = x, we write x n x.
