Unique Fixed Point Theorem in Complete Cone Metric Spaces
[1]
K. Prudhvi, Department of Mathematics, University College of Science, Saifabad, Osmania University, Hyderabad, Telangana State, India.
In this paper, we prove a unique fixed point theorem in complete cone metric spaces without assuming the normality condition. Our result extends and improves recent result of [Sh. Rezapour and R. Hamlbarani, Some notes on the paper cone metric spaces and fixed point theorem of contractive mappings, J. Math. Anal. Appl., 345(2008), 719-724].
Cone Metric Space, Contractive Condition, Fixed Point, Normal Cone
[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 incone metric spaces, Appl. Math. Lett., 22(2009) 511-515.
[3]
I. Altun, G. Durmaz, Some fixed point theorems on orderedcone metric spaces, Rend. Ciric. Mat. Palermo 58(2009)319-325.
[4]
M.Arshad, A.Azam, P.vetro, Some common fixed point resultson cone metric spaces, Fixed Point Theory Appl., (2009)11, Article ID 493965.
[5]
C.Di Bari and P.Vetro, 𝜑-pairs and common fixed points in cone metric spaces, Rendicontidel Circolo Mathematico diPalermo, Vol. 57(2008) 279-285.
[6]
P.N.Dutta and B.S.Choudary, A generalization of contractionprinciple in metric spaces, Fixed Point Theory Appl. 2008(2008), Article ID 406386, 8 pages.
[7]
L. G.Huang, X. Zhang, Cone metric spaces and fixed pointtheorems of contractive mappings,J. Math. Anal. Appl.332(2)(2007)1468-1476.
[8]
D. IIic,V. Rakocevic, Common fixed points for maps on cone metric space, J. Math. Anal. Appl. 341(2008)876-882.
[9]
S.H.Kim and B.S.Lee, Generalized fixed point theorems in cone metric spaces, Korean J. Math. 20(2012), No.3, pp., 353-360.
[10]
K. Prudhvi, A fixed point theorem of expanding onto mappings in generalized contractive condition in completecone metric spaces, Open Science Journal of Mathematics andApplication, 3(3) (2015),89-91.
[11]
Sh.Rezapour and R.Hamlbarani, Some notes on the paper conemetric spaces and fixed point theorem of contractive mappings, J.Math. Anal. Appl. 345(2008)719-724.
[12]
P.Vetro, Common fixed points in cone metric spaces, Rend.Circ. Mat. Palermo. 56(2007) 464-468.
