TY - JOUR JF - IJMSI JO - IJMSI VL - 15 IS - 1 PY - 2020 Y1 - 2020/4/01 TI - The Banach Type Contraction for Mappings on Algebraic Cone Metric Spaces Associated with An Algebraic Distance and Endowed with a Graph TT - N2 - 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. SP - 41 EP - 52 AU - Fallahi, K. AU - Soleimani Rad, Gh. AD - Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran KW - Algebraic cone metric space KW - Algebraic distance KW - Banach contraction KW - Orbitally G-continuous mapping UR - http://ijmsi.ir/article-1-1064-en.html DO - 10.29252/ijmsi.15.1.41 ER -