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PARTIAL CONE METRIC SPACE AND SOME FIXED POINT THEOREMS

Year 2013, Volume: 3 Issue: 1, 1 - 9, 01.06.2013

Abstract

In the present paper, we have proved some convergence properties of a sequence of elements in a partial cone metric space and thereby we have established some fixed point theorems on it.

References

  • [1] Banach, S., (1922), Sur les operations dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math., 3 ,133-181 (French).
  • [2] Chatterjee, S. K., (1972), Fixed point theorems, Rend. Acad. Bulgare Sc., 25, 727-730.
  • [3] Huang, L.-G. and Zhang, X., (2007), Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332(2), 1468-1476.
  • [4] Kannan, R., (1968), Some results on fixed points, Bull. Calcutta Math. Soc., 60, 71-76.
  • [5] K¨unzi, H.P.A., (Dordrecht, 2001), Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology, Handbook of the History of General Topology (eds. C.E. Aull and R. Lowen), Kluwer Acad. Publ., 3, 853-968.
  • [6] Lin, S.D., (1987), A common fixed point theorem in abstract spaces, Indian Journal of Pure and Applied Mathematics, 18(8), 685-690.
  • [7] Matthews, S., (1994), Partial Metric Topology, Proceedings of the 8th Summer Conference on Topology and its Applications, Annals of The New york Academy of Sciences, 728, 183-197.
  • [8] Bukatin, M., Kopperman, R., Matthews, S. and Pajoohesh, H., (october, 2009), Partial Metric Spaces, The Mathematical Association of America, 116, 708-718.
  • [9] Reich, S., (1971), Kannan’s fixed point thorem, Boll. Un. Math. Ital., 4, 1-11.
  • [10] Romaguera, S. and Schellekens, M., (2003), Weightable quasi-metric semigroups and semilattices, Proc. MFCSIT2000, Electronic Notes in Theoretical Computer Science, 40, 12 pages.
  • [11] Rzepecki, B., (1980), On fixed point theorems of Maia type, Publications de lInstitut Mathematique, 28(42), 179-186.
  • [12] S¨onmez, A., (14 Jan, 2011), Fixed point theorems in partial cone metric spaces, arXiv:1101.2741v1 [math.GN].
  • [13] Valero, O., (2005), On Banach fixed point theorems for partial metric spaces, Appl. Gen. Top, 6(2), 229-240.
Year 2013, Volume: 3 Issue: 1, 1 - 9, 01.06.2013

Abstract

References

  • [1] Banach, S., (1922), Sur les operations dans les ensembles abstraits et leur application aux quations intgrales, Fund. Math., 3 ,133-181 (French).
  • [2] Chatterjee, S. K., (1972), Fixed point theorems, Rend. Acad. Bulgare Sc., 25, 727-730.
  • [3] Huang, L.-G. and Zhang, X., (2007), Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332(2), 1468-1476.
  • [4] Kannan, R., (1968), Some results on fixed points, Bull. Calcutta Math. Soc., 60, 71-76.
  • [5] K¨unzi, H.P.A., (Dordrecht, 2001), Nonsymmetric distances and their associated topologies: About the origins of basic ideas in the area of asymmetric topology, Handbook of the History of General Topology (eds. C.E. Aull and R. Lowen), Kluwer Acad. Publ., 3, 853-968.
  • [6] Lin, S.D., (1987), A common fixed point theorem in abstract spaces, Indian Journal of Pure and Applied Mathematics, 18(8), 685-690.
  • [7] Matthews, S., (1994), Partial Metric Topology, Proceedings of the 8th Summer Conference on Topology and its Applications, Annals of The New york Academy of Sciences, 728, 183-197.
  • [8] Bukatin, M., Kopperman, R., Matthews, S. and Pajoohesh, H., (october, 2009), Partial Metric Spaces, The Mathematical Association of America, 116, 708-718.
  • [9] Reich, S., (1971), Kannan’s fixed point thorem, Boll. Un. Math. Ital., 4, 1-11.
  • [10] Romaguera, S. and Schellekens, M., (2003), Weightable quasi-metric semigroups and semilattices, Proc. MFCSIT2000, Electronic Notes in Theoretical Computer Science, 40, 12 pages.
  • [11] Rzepecki, B., (1980), On fixed point theorems of Maia type, Publications de lInstitut Mathematique, 28(42), 179-186.
  • [12] S¨onmez, A., (14 Jan, 2011), Fixed point theorems in partial cone metric spaces, arXiv:1101.2741v1 [math.GN].
  • [13] Valero, O., (2005), On Banach fixed point theorems for partial metric spaces, Appl. Gen. Top, 6(2), 229-240.
There are 13 citations in total.

Details

Primary Language English
Journal Section Research Article
Authors

D. Dey This is me

M. Saha This is me

Publication Date June 1, 2013
Published in Issue Year 2013 Volume: 3 Issue: 1

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