Document Type: Research Paper


Department of Mathematics, Payame Noor University, Tehran, Iran


In this paper, we prove some properties of algebraic cone metric spaces and introduce 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.


Main Subjects

[1] Y. J. Cho, R. Saadati, S. H. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl. 61 (2011), 1254-1260.

[2] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, 1985.

[3] M. Dordevic, D. Doric, Z. Kadelburg, S. Radenovic, D. Spasic, Fixed point results under  c-distance in tvs-cone metric spaces, Fixed Point Theory Appl. (2011), 2011:29.

[4] W. S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal. 72 (5) (2010), 2259-2261.

[5] L. G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), 1467-1475.

[6] S. Jankovic, Z. Kadelburg, S. Radenovic, On cone metric spaces, a survey, Nonlinear Anal. 74 (2011), 2591- 2601.

[7] G. S. Jeong, B. E. Rhoades, Maps for which F (T ) = F (T n), Fixed Point Theory Appl. 6 (2005), 87-131.

[8] O. Kada, T. Suzuki, W. Takahashi, Nonconvex minimization theorems and fixed point theorems in complete metric spaces, Math. Japon. 44 (1996), 381-391.

[9] A. Niknam, S. Shamsi Gamchi, M. Janfada, Some results on TVS-cone normed spaces and algebraic cone metric spaces, Iranian J. Math. Sci. Inf. 9 (1) (2014), 71-80.

[10] H. Rahimi, G. Soleimani Rad, Common fixed-point theorems and c-distance in ordered cone metric spaces, Ukrain. Math. J. 65 (12) (2014), 1845-1861.

[11] H. Rahimi, G. Soleimani Rad, S. Radenovi´c, Algebraic cone b-metric spaces and its equivalence, Miskolc. Math. Notes. 17 (1) (2016), 553-560.

[12] S. Rezapour, R. Hamlbarani, Some note on the paper cone metric spaces and fixed point theorems of con- tractive mappings, J. Math. Anal. Appl. 345 (2008), 719-724.

[13] P. P. Zabrejko, K-metric and K-normed linear spaces: survey, Collect. Math. 48 (1997), 825-859.