# A unique tripled common fixed point theorem for four mappings in partial metric spaces.

Received: January 15, 2013. Revised: May 21, 2013.

2000 Mathematics Subject Classification: 54H25, 47H10, 54E50.

REFERENCES

[1] T. Abdeljawad, E. Karapinar and K. Tas: Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24(2011), No. 11, 1894-1899.

[2] I. Altun, F. Sola and H. Simsek: Generalized contractions on partial metric spaces, Topology Appl., 157(2010), No. 18, 2778-2785.

[3] I. Altun and A. Erduran: Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., Vol. 2011, Article ID 508730, 10 pages.

[4] H. Aydi: Some coupled fixed point results on partial metric spaces, Internat. J. Math. Math. Sci., Vol. 2011, Article ID 647091, 11 pages.

[5] H. Aydi: Fixed point results for weakly contractive mappings in ordered partial metric spaces, J. Adv. Math. Stud., 4(2011), No. 2, 1-12.

[6] H. Aydi, E. Karapinar and M. Postolache: Tripled coincidence point theorems for weak [phi]-contractions in partially ordered metric spaces, Fixed Point Theory Appl., Vol. 2012, Article ID 2012:44, 12 pages.

[7] V.Berinde and M.Borcut: Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74(2011), No. 15, 4889-4897.

[8] T. G. Bhaskarand V. Lakshmikantham: Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65(2006), 1379-1393.

[9] Lj. Ciric, B. Samet, H. Aydi and C. Vetro: Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218(2011), 2398-2406.

[10] R. Heckmann: Approximation of metric spaces by partial metric spaces, Appl. Categ. Struct., 7(1999), No. 1-2, 71-83.

[11] D. Ilic, V. Pavlovicand V. Rakocevk:: Some new extensions of Banach's contraction principle to partial metric spaces, Appl. Math. Lett., 24(2011), No. 8, 1326-1330.

[12] E. Karapinar and I. M. Erhan: Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24(2011), No. 11, 1900-1904.

[13] E. Karapinar: Weak [phi]-contraction on partial contraction, J. Comput. Anal. Appl. (in press).

[14] E. Karapinar: Weak [phi]-contraction on partial contraction and existence of fixed points in partially ordered sets, Mathematica Aeterna, 1(2011), No. 4, 237-244.

[15] E. Karapinar: Generalizations of Caristi Kirk's theorem on partial metric spaces, Fixed Point Theory Appl., Vol. 2011, Article ID 2011:4.

[16] R. Kopperman, S. G. Matthews and H. Pajoohesh: What do partial metrics represent?, Spatial representation: discrete vs. continuous computational models, Dagstuhl Seminar Proceedings, No. 04351, Internationales Begegnungs- und Forschungszentrum fur Informatik (IBFI), Schloss Dagstuhl, Germany, (2005).

[17] H.P.A. Kunzi, H. Pajoohesh and M. P. Schellekens: Partial quasi-metrics, Theoret. Comput. Sci., 365(2006), No. 3, 237-246.

[18] V. Lakshmikantham and Lj. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70(2009), 4341-4349.

[19] S. G. Matthews: Partial metric topology, Research Report 212. Dept. of Computer Science. University of Warwick, 1992.

[20] S. G. Matthews: Partial metric topology, in Proceedings of the 8th Summer Conference on General Topology and Applications, vol. 728, pp. 183-197, Annals of the New York Academy of Sciences, 1994.

[21] S. Oltra and O. Valero: Banach's fixed point theorem for partial metric spaces, Rendiconti dell'Istituto di Matematica dell'Universitadi Trieste., 36(2004), No. 1-2, 17-26.

[22] S. J. ONeill: Two topologies are better than one, Tech. report, University of Warwick, Coventry, UK, http://www.dcs.warwick.ac.uk/reports/283.html, (1995).

[23] K.P.R. Rao and G.N.V. Kishore: A unique common fixed point theorem for four maps under ip-<fi contractive condition in partial metric spaces, Bull. Math. Anal. Appl., 3(2011), No. 3, 56-63.

[24] K.P.R. Rao and G.N.V. Kishore: A unique common triple fixed point theorem in partially ordered cone metric spaces, Bull. Math. Anal. Appl., 3(2011), No. 4, 213-222.

[25] K.P.R. Rao, G.N.V. Kishore and N.Srinivasa Rao: A unique common 3--tupled fixed point theorem for [psi]-[phi] contractions in partial metric spaces, Mathematica Aeterna, 1(2011), No. 7, 491-507.

[26] S. Romaguera and M. Schellekens: Weightable quasi-metric semigroup and semilattices, Electronic Notes Theor. Comput. Sci., Proceedings of MFCSIT, 40, Elsevier, (2003).

[27] S. Romaguera: A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl., Vol. 2010, Article ID 493298, 6 pages.

[28] M. Schellekens: The Smyth completion: a common foundation for denotational semantics and complexity analysis, Electronic Notes Theor. Comput. Sci., 1(1995), 535-556.

[29] M. P. Schellekens: A characterization of partial metrizability: domains are quantifiable, Theor. Comput. Sci., 305(2003), No. 1-3, 409-432.

[30] O. Valero: On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol., 6(2005), No. 2, 229-240.

[31] P. Waszkiewicz: Quantitative continuous domains, Appl. Categ. Struct., 11(2003), No. 1, 41-67.

[32] P. Waszkiewicz: Partial metrizebility of continuous posets, Math. Struct. Comput Sci., 16(2006), No. 2, 359-372.

Acharya Nagarjuna University

Department of Mathematics

Nagarjuna Nagar, Guntur--522510, Andhra Pradesh, India

E-mail address: kprrao2004@yahoo.com

Baba Institute of Technology and Sciences

Department of Mathematics

P. M. Palem, Madhurawada--530048, Visakhapatnam District, Andhra Pradesh, India

E-mail address: kishore.apr2@gmail.com

Aligarh Muslim University

Department of Mathematics

Aligarh-202002, U.P.

E-mail address: mhimdad@yahoo.co.in

2000 Mathematics Subject Classification: 54H25, 47H10, 54E50.

REFERENCES

[1] T. Abdeljawad, E. Karapinar and K. Tas: Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett., 24(2011), No. 11, 1894-1899.

[2] I. Altun, F. Sola and H. Simsek: Generalized contractions on partial metric spaces, Topology Appl., 157(2010), No. 18, 2778-2785.

[3] I. Altun and A. Erduran: Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., Vol. 2011, Article ID 508730, 10 pages.

[4] H. Aydi: Some coupled fixed point results on partial metric spaces, Internat. J. Math. Math. Sci., Vol. 2011, Article ID 647091, 11 pages.

[5] H. Aydi: Fixed point results for weakly contractive mappings in ordered partial metric spaces, J. Adv. Math. Stud., 4(2011), No. 2, 1-12.

[6] H. Aydi, E. Karapinar and M. Postolache: Tripled coincidence point theorems for weak [phi]-contractions in partially ordered metric spaces, Fixed Point Theory Appl., Vol. 2012, Article ID 2012:44, 12 pages.

[7] V.Berinde and M.Borcut: Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal., 74(2011), No. 15, 4889-4897.

[8] T. G. Bhaskarand V. Lakshmikantham: Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65(2006), 1379-1393.

[9] Lj. Ciric, B. Samet, H. Aydi and C. Vetro: Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput., 218(2011), 2398-2406.

[10] R. Heckmann: Approximation of metric spaces by partial metric spaces, Appl. Categ. Struct., 7(1999), No. 1-2, 71-83.

[11] D. Ilic, V. Pavlovicand V. Rakocevk:: Some new extensions of Banach's contraction principle to partial metric spaces, Appl. Math. Lett., 24(2011), No. 8, 1326-1330.

[12] E. Karapinar and I. M. Erhan: Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett., 24(2011), No. 11, 1900-1904.

[13] E. Karapinar: Weak [phi]-contraction on partial contraction, J. Comput. Anal. Appl. (in press).

[14] E. Karapinar: Weak [phi]-contraction on partial contraction and existence of fixed points in partially ordered sets, Mathematica Aeterna, 1(2011), No. 4, 237-244.

[15] E. Karapinar: Generalizations of Caristi Kirk's theorem on partial metric spaces, Fixed Point Theory Appl., Vol. 2011, Article ID 2011:4.

[16] R. Kopperman, S. G. Matthews and H. Pajoohesh: What do partial metrics represent?, Spatial representation: discrete vs. continuous computational models, Dagstuhl Seminar Proceedings, No. 04351, Internationales Begegnungs- und Forschungszentrum fur Informatik (IBFI), Schloss Dagstuhl, Germany, (2005).

[17] H.P.A. Kunzi, H. Pajoohesh and M. P. Schellekens: Partial quasi-metrics, Theoret. Comput. Sci., 365(2006), No. 3, 237-246.

[18] V. Lakshmikantham and Lj. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70(2009), 4341-4349.

[19] S. G. Matthews: Partial metric topology, Research Report 212. Dept. of Computer Science. University of Warwick, 1992.

[20] S. G. Matthews: Partial metric topology, in Proceedings of the 8th Summer Conference on General Topology and Applications, vol. 728, pp. 183-197, Annals of the New York Academy of Sciences, 1994.

[21] S. Oltra and O. Valero: Banach's fixed point theorem for partial metric spaces, Rendiconti dell'Istituto di Matematica dell'Universitadi Trieste., 36(2004), No. 1-2, 17-26.

[22] S. J. ONeill: Two topologies are better than one, Tech. report, University of Warwick, Coventry, UK, http://www.dcs.warwick.ac.uk/reports/283.html, (1995).

[23] K.P.R. Rao and G.N.V. Kishore: A unique common fixed point theorem for four maps under ip-<fi contractive condition in partial metric spaces, Bull. Math. Anal. Appl., 3(2011), No. 3, 56-63.

[24] K.P.R. Rao and G.N.V. Kishore: A unique common triple fixed point theorem in partially ordered cone metric spaces, Bull. Math. Anal. Appl., 3(2011), No. 4, 213-222.

[25] K.P.R. Rao, G.N.V. Kishore and N.Srinivasa Rao: A unique common 3--tupled fixed point theorem for [psi]-[phi] contractions in partial metric spaces, Mathematica Aeterna, 1(2011), No. 7, 491-507.

[26] S. Romaguera and M. Schellekens: Weightable quasi-metric semigroup and semilattices, Electronic Notes Theor. Comput. Sci., Proceedings of MFCSIT, 40, Elsevier, (2003).

[27] S. Romaguera: A Kirk type characterization of completeness for partial metric spaces, Fixed Point Theory Appl., Vol. 2010, Article ID 493298, 6 pages.

[28] M. Schellekens: The Smyth completion: a common foundation for denotational semantics and complexity analysis, Electronic Notes Theor. Comput. Sci., 1(1995), 535-556.

[29] M. P. Schellekens: A characterization of partial metrizability: domains are quantifiable, Theor. Comput. Sci., 305(2003), No. 1-3, 409-432.

[30] O. Valero: On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol., 6(2005), No. 2, 229-240.

[31] P. Waszkiewicz: Quantitative continuous domains, Appl. Categ. Struct., 11(2003), No. 1, 41-67.

[32] P. Waszkiewicz: Partial metrizebility of continuous posets, Math. Struct. Comput Sci., 16(2006), No. 2, 359-372.

Acharya Nagarjuna University

Department of Mathematics

Nagarjuna Nagar, Guntur--522510, Andhra Pradesh, India

E-mail address: kprrao2004@yahoo.com

Baba Institute of Technology and Sciences

Department of Mathematics

P. M. Palem, Madhurawada--530048, Visakhapatnam District, Andhra Pradesh, India

E-mail address: kishore.apr2@gmail.com

Aligarh Muslim University

Department of Mathematics

Aligarh-202002, U.P.

E-mail address: mhimdad@yahoo.co.in

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Author: | Rao, K.P.R.; Kishore, G.N.V.; Imdad, M. |
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Publication: | Journal of Advanced Mathematical Studies |

Article Type: | Author abstract |

Geographic Code: | 9INDI |

Date: | Jul 1, 2013 |

Words: | 863 |

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