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In this work, we define the notion of algebraic distance in alge- braic cone metric spaces defined 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 fixed point for a Banach contractive type mapping in algebraic cone metric spaces associated with an algebraic dis- tance and endowed with a graph. [ABSTRACT FROM AUTHOR]

In this paper, we prove some properties of algebraic cone metric spaces and in- troduce the notion of algebraic distance in an algebraic cone metric space. As an application, we obtain some famous fixed point results in the framework of this algebraic distance. [ABSTRACT FROM AUTHOR]

We define several variants of algebraic distance in an algebraic cone metric space. Then we obtain some new results about their properties and compare these definitions. [ABSTRACT FROM AUTHOR]