The Banach Type Contraction for mappings on Algebraic Cone Metric Spaces Associated with an Algebraic Distance and Endowed with a Graph

In this work, we dene the notion of algebraic distance in alge- braic cone metric spaces dened by Niknam et al. [A. Niknam, S. Shamsi Gamchi and M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Infor. 9 (1) (2014) 71{80] and introduce some its elementary properties. Then we prove the existence and uniqueness of xed point for a Banach contractive type mapping in algebraic cone metric spaces associated with an algebraic dis- tance and endowed with a graph.