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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.

Details

Primary Language English
Journal Section Research Article
Authors

D. DEY This is me
Koshigram Union Institution, Koshigram-713150, Burdwan, West Bengal, India


M. SAHA This is me
Department of Mathematics,The University of Burdwan, Burdwan-713104, West Bengal, India

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

Cite

Bibtex @ { twmsjaem761691, journal = {TWMS Journal of Applied and Engineering Mathematics}, issn = {2146-1147}, eissn = {2587-1013}, address = {Işık University ŞİLE KAMPÜSÜ Meşrutiyet Mahallesi, Üniversite Sokak No:2 Şile / İstanbul}, publisher = {Turkic World Mathematical Society}, year = {2013}, volume = {3}, number = {1}, pages = {1 - 9}, title = {PARTIAL CONE METRIC SPACE AND SOME FIXED POINT THEOREMS}, key = {cite}, author = {Dey, D. and Saha, M.} }