Cone 2- Metric Spaces  and  Fixed Point Theorems for Pair of Contractive Maps

S. K. Tiwari

S. K. Tiwari Department of Mathematics, Dr. C.V. Raman University, Bilaspur (C.G.), India

Keywords: Fixed point, Cone 2- metric space, Contractive mapping, Ordered Banach space.

Abstract

We review, generalize and prove some fixed point theorems for contractive maps in cone 2- metric spaces.

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References

Banach’s.(1922), Sur les operations dans les ensembles abstraits et leur applications aux equations integrals, fundamental athematicae,3(7), 133-181.

S. Gahler, 2-metricsche Raume und ihre topologische structure, Math. Nachr. 26(1963),115-148.

S. Gahler, Uber die Uniformisierbarkeit 2-metricsche Raume, Math. Nachr. 28(1995),235-244.

S. Gahler, Zur geometric 2-2-metricsche Raume, Revne Roumaine der Mathem. Pures etAppliques, 11(1966), 665-667.

K. Iseki, Fixed point theorems in 2-metric spaces, Math. Seminar Notes, Kobe Univ., 3 (1975), 133-136.

K. Iseki, P. L. Sharma and B. K. Sharma, Contraction type mapping on 2- metric spaces, Math. Japonicae, 21 (1976), 67-70.

K. Iseki, Fixed point theorems in Banach spaces, Math. Seminar Notes, Kobe Univ.,2 (1976), 11-13.

L. G. Huang, X. Zhang, Cone metric spaces and Fixed point theorems for contractive mappings, J. of Math. Anal. and App., 332(2007), 1468-1476.

Sh. Rezapour and R. Hamlbarani, Some notes on the paper “cone metric spaces and fixed point theorems of contractive mappings”,J. Math. Anal. Appl. 345 (2008) 719-724.

S. H. Cho, Fixed point theorems for generalized contractive mappings on cone metric space, Int. J. Of Math. Analysis. 6(50), (2012), 2473-2481.

S. K. Tiwari, R. P. Dubey and A. K. Dubey, Cone metric spaces and fixed Point Theorems for pair of generalized contractive mappings, Int. J. Of Math. Research, 5(1) (2013, 77- 85.

S. K. Tiwari, R. P. Dubey and A. K. Dubey, Common fixed point results in cone metricSpaces, Int. J. Of Math. Research, 2(3) (2013), 352-355.

Tiwari, S.K. and R. P. Dubey (2013) , An extension of the paper “some fixedpoint theorems for generalized contractive mappings in cone metric spaces”, Int. J. of Math.Archive--4(12) 112-115.

A. K. Dubey, R. Shukla, R. P. Dubey, Cone metric spaces and Fixed pointresults of Generalized contractive mappings, Advances in fixed point theory,3(3), (2013), 568-577.

B. Singh, S. Jain and P. Bhagat, Cone 2- Metric space and fixed point theorem of contractive mapping,(2012), 52(2), 143-151.

D. Ilic, and V. Rakocevic, Quasi contraction on cone metric space, Applied Mathematics Letters 22(2009), 728-731.