American Journal of Mathematical Analysis
ISSN (Print): 2333-8490 ISSN (Online): 2333-8431 Website: http://www.sciepub.com/journal/ajma Editor-in-chief: Grigori Rozenblum
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American Journal of Mathematical Analysis. 2015, 3(1), 5-9
DOI: 10.12691/ajma-3-1-2
Open AccessArticle

Common Fixed Point Theorems for Two Self-maps in Cone Metric Spaces under Different Contractive Conditions

P. Rama Bhadra Murthy1, and M. Rangamma1

1Department of Mathematics, University College of Science, Osmania University, Hyderabad, India

Pub. Date: January 27, 2015

Cite this paper:
P. Rama Bhadra Murthy and M. Rangamma. Common Fixed Point Theorems for Two Self-maps in Cone Metric Spaces under Different Contractive Conditions. American Journal of Mathematical Analysis. 2015; 3(1):5-9. doi: 10.12691/ajma-3-1-2

Abstract

The existence of unique common fixed point theorems for two weakly compatible self-maps satisfying different contractive conditions in cone metric spaces without using normality.

Keywords:
weakly compatible maps common fixed points cone metric spaces coincidence points

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References:

[1]  B.E.Rhoades, “A comparision of various definitions of contractive mappings”, Trans.Amer.Math.Soc.26(1977) 257-290.
 
[2]  Paula Collaco and Jaime Carvalho E Silva, “A complete comparision of 25 contraction conditions”, Nonlinear Analysis, Theory, Methods and Applications, Vol.30, No.1, pp. 471-476.
 
[3]  L.G.Huang, X.Zhang, “Cone metric spaces and fixed point theorems of contractive mappings”, J.Math.Anal.Appl.332(2) (2007) 1468-1476.
 
[4]  M.Abbas and G. Jungck, “Common fixed point results for non-commutating mappings withour continuity in cone metric spaces”, J.Math.Anal.Appl. 341(2008)416-420.
 
[5]  M.Abbas and B.E.Rhoades, “Fixed and Periodic point results in Cone metric spaces”, Appl.Math.Lett.22(2009), 511-515.
 
[6]  S.Rezapour and Halmbarani, “Some notes on the paper “cone metric spaces and fixed point theorems of contractive mappings”,J.Math.Anal.Appl.345(2008)719-729.
 
[7]  S.Rezapour, R.H.Hagi, “Fixed points of multi functions on cone metric spaces”, Number.Funct.Anal. 30(7-9)(2009)825-832.
 
[8]  Stojan Radenovic, “Common fixed points under contractive conditions in cone metric spaces”, Computers and Mathematics with Applications. 58(2009)1273-1278.
 
[9]  Vetro, “Common fixed points in cone meric spaces”, Rend.Ciric. Mat.Palermo. 56(2007)464-468.
 
[10]  T.Abdeljawad, E.Karapinar and K.Tas, “Common fixed point theorems in cone Banach spaces”, Hacet. J.Math.Stat. 40(2011), 211-217.
 
[11]  Jankovic, S.Dadelburg, Z.Radenovic, “On cone metric spaces, A survey”, Nonlinear Analysis, 74(2011), 2591-2601.
 
[12]  P.Raja, S.M.Vaezpour, “Some extensions of Banach’s contraction principle in complete cone metric spaces”, Fixed Point Theory and Applications, Article ID768294(2008), 11pages.