RT - Journal Article T1 - The Banach Type Contraction for Mappings on Algebraic Cone Metric Spaces Associated with An Algebraic Distance and Endowed with a Graph JF - IJMSI YR - 2020 JO - IJMSI VO - 15 IS - 1 UR - http://ijmsi.ir/article-1-1064-en.html SP - 41 EP - 52 K1 - Algebraic cone metric space K1 - Algebraic distance K1 - Banach contraction K1 - Orbitally G-continuous mapping AB - In this work, we define the notion of an algebraic distance in algebraic 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 distance and endowed with a graph. LA eng UL http://ijmsi.ir/article-1-1064-en.html M3 10.29252/ijmsi.15.1.41 ER -