American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: Editor-in-chief: Grigori Rozenblum
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American Journal of Mathematical Analysis. 2013, 1(2), 25-27
DOI: 10.12691/ajma-1-2-2
Open AccessArticle

Common Fixed Points in Cone Metric Spaces

K. Prudhvi1,

1Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, Andhra Pradesh, India.

Pub. Date: April 23, 2013

Cite this paper:
K. Prudhvi. Common Fixed Points in Cone Metric Spaces. American Journal of Mathematical Analysis. 2013; 1(2):25-27. doi: 10.12691/ajma-1-2-2


In this paper, we prove a unique common fixed point theorem in cone metric spaces without appealing to commutativity conditions. These results generalize several well-known comparable results in the literature.

common fixed point cone metric space coincidence points

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[1]  M. Abbas and G. Jungck, Common fixed point results for non commuting mappings without continuity in cone metric spaces.J. Math. Anal. Appl. 341(2008) 416-420.
[2]  M.Abbas and B.E.Rhoades, Fixed and periodic point results in cone metric spaces. Appl. Math. Lett. 22 (2009), 511-515.
[3]  Issk Altun, G.Durmaz, Some fixed point theorems on ordered cone metric spaces, Rend. Circ. Mat. Palermo 58 (2009) 319-325.
[4]  Hardy, G.E., Roggers, T.D. A generalization of a fixed point theorem of Reich, Canad. Math. Bull., 16(2) (1973), 201- 206.
[5]  L.G.Huang, X.Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J.Math. Anal. Appl. 332(2) (2007)1468-1476.
[6]  J.Gornicki, B.E.Rhoades, A general fixed point theorem for involutions, Indian J.Pure Appl. Math.27 (1996) 13-23.
[7]  llic, D., Rakocevic, V. Common fixed points for maps on cone metric space, J.Math. Anal. Appl., 341 (2008), 876-882.
[8]  G.Jungck, Commuting maps and fixed points, Internat.J.Maths. Sci.9 (4) (1986) 771-779.
[9]  G.Jungck, common fixed points for non continuous non self maps on non-metric spaces, Far East J.Math.Sci. (FEJMS) 4(1996) 199-215.
[10]  G.J.ungck and B.E.Rhoades, fixed point for set valued functions without continuity, Indian J.Pure Appl. Math. 29(3)(1998) 227-238.
[11]  R.Kannan, some results on fixed points, Bull.Calcutta Math.Soc. 60(1968)71-76.
[12]  R.P.Pant. Common fixed points of noncommuting mappings, J.Math. Anal. Appl., 188(1994), 436-440.
[13]  Reich, S. Some remarks concerning contraction mappings, Canad. Math. Bull., 14(2) (1971), 121-124.
[14]  S.Rezapour and Halbarani, Some notes on the paper “cone metric spaces and fixed point theorem of contractive mappings “, J. Math. Anal. Appl. 345(2008), 719-724.
[15]  S.Rezapour ,R.H.Hagi , Fixed of multi functions on cone metric spaces, Number.Funct.Anal.30 (7-9) (2009) 825-832.
[16]  B.E.Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer .Math. soc. 26(1977) 257-290.
[17]  Sessa, S. On a weak commutativity condition of mappings in fixed point considerations, Publ. Inst. Math., 32(1982), 149-153.
[18]  Stojan Radenović, Common fixed points under contractive conditions in cone metric spaces, Computers and Mathematics with Applications 58 (2009) 1273-1278.
[19]  Vetro, P.:Common fixed points in cone metric spaces, Rend. Ciric. Mat. Palermo. 56 (2007), 464-468.