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SOME FIXED POINT THEOREMS IN PARTIAL METRIC SPACES

Year 2013, Volume 3, Issue 2, 206 - 213, 01.12.2013

Abstract

Here we prove two fixed point theorems on partial metric space, which was defined by S. Matthews [8] in 1994. In the literature one can find fixed point theorems proved on such spaces by using Picard iteration schemes. Here our main ingredient is Cantor intersection type results.

References

  • [1] Hassen Aydi, Some Fixed Point Results in ordered partial metric spaces, Math. GN(2011),1–7.
  • [2] S. Banach, Sur les operations dans ensembles abstraits et. leur application aux quations integrals, Fund .Math.3,(1922)133181(French).1,3.
  • [3] Michael Bukatin ET. A L., Partial Metric Spaces, The Mathematical Association of America, Monthly 116, 708–718.
  • [4] L. B. Ciric, Generalised contractions and fixed point theorems, Publ. Inst. Math. 12(1971), 20–26.
  • [5] S.K. Chatterjee, Fixed point theorems, Rend Acad. Bulgare Sc.25,(1972), 727–730.
  • [6] E. Karapinar, Generalisations of Cristi Kirk’s Theorem on Partial Metric Spaces, Fixed Point Theory Appl. 2011, 2011:4, 7pp.
  • [7] R. Kannan, Some results on fixed points, Bull. Calcutta Math.Soc. 60(1968),71–76.
  • [8] S. Matthews, Partial Metric Topology, Proceedings of the 8thsummer conference on Topology and its applications, Annals of The New York Academy of Sciences, 728(1994), 183–197.
  • [9] S.J. O’Neill, Two topologies are better than one, Tech. report, University of Warwick, Conventry, UK, 1995.
  • [10] S. J. O’Neill, Partial Metrics, valuations and domain theory, Proc. 11th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci. 806(1996) 304–315.
  • [11] O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Top 6(2) (2005), 229–240.
  • [12] S. Oltra, O. Volero, Banach’s fixed point theorem for partial metric spaces, Rend. 1st.Mat. Univ.Triesta 36(2004), 17–26.

Year 2013, Volume 3, Issue 2, 206 - 213, 01.12.2013

Abstract

References

  • [1] Hassen Aydi, Some Fixed Point Results in ordered partial metric spaces, Math. GN(2011),1–7.
  • [2] S. Banach, Sur les operations dans ensembles abstraits et. leur application aux quations integrals, Fund .Math.3,(1922)133181(French).1,3.
  • [3] Michael Bukatin ET. A L., Partial Metric Spaces, The Mathematical Association of America, Monthly 116, 708–718.
  • [4] L. B. Ciric, Generalised contractions and fixed point theorems, Publ. Inst. Math. 12(1971), 20–26.
  • [5] S.K. Chatterjee, Fixed point theorems, Rend Acad. Bulgare Sc.25,(1972), 727–730.
  • [6] E. Karapinar, Generalisations of Cristi Kirk’s Theorem on Partial Metric Spaces, Fixed Point Theory Appl. 2011, 2011:4, 7pp.
  • [7] R. Kannan, Some results on fixed points, Bull. Calcutta Math.Soc. 60(1968),71–76.
  • [8] S. Matthews, Partial Metric Topology, Proceedings of the 8thsummer conference on Topology and its applications, Annals of The New York Academy of Sciences, 728(1994), 183–197.
  • [9] S.J. O’Neill, Two topologies are better than one, Tech. report, University of Warwick, Conventry, UK, 1995.
  • [10] S. J. O’Neill, Partial Metrics, valuations and domain theory, Proc. 11th Summer Conference on General Topology and Applications. Ann. New York Acad. Sci. 806(1996) 304–315.
  • [11] O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Top 6(2) (2005), 229–240.
  • [12] S. Oltra, O. Volero, Banach’s fixed point theorem for partial metric spaces, Rend. 1st.Mat. Univ.Triesta 36(2004), 17–26.

Details

Primary Language English
Journal Section Research Article
Authors

Mukti GANGOPADHYAY This is me
Calcutta Girls B.T. College, 6/1, Swinhoe Street , Kolkata 700019, India


M. SAHA This is me
Department of Mathematics, The University of Burdwan, Burdwan –713104, India.


A.p. BAİSNAB This is me
Lady Brabourne College, Kolkata, India.

Publication Date December 1, 2013
Published in Issue Year 2013, Volume 3, Issue 2

Cite

Bibtex @ { twmsjaem761411, 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 = {2}, pages = {206 - 213}, title = {SOME FIXED POINT THEOREMS IN PARTIAL METRIC SPACES}, key = {cite}, author = {Gangopadhyay, Mukti and Saha, M. and Baisnab, A.p.} }