Tripled Coincidence Points of Mappings in Partially Ordered 0-Complete Partial Metric Spaces

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Vesna Cojbasic Rajic, Tripled Coincidence Points of Mappings in Partially Ordered 0-Complete Partial Metric Spaces, Int. J. Anal. Appl., 2 (2) (2013), 79-110.

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Vesna Cojbasic Rajic

Abstract

In this paper, we introduce the concept of a tripled coincidence point for a pair of nonlinear contractive mappings F : X3 → X and g : X → X in partially ordered 0-complete partial metric spaces and obtain existence and uniqueness theorems. Our results generalize, extend, unify and complement recent tripled coincidence point theorems established by Marin Borcut, Vasile Berinde [M. Borcut, V. Berinde, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Applied Mathematical and Computation 218 (2012) 5929-5935], Marin Borcut [M. Borcut, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Applied Mathematical and Computation 218 (2012) 7339-7346], Hassen Aydi, Erdal Karapinar, Mihail Postolache [H. Aydi, E. Karapinar, M. Postolache, Tripled coincidence point theorems for weak φ-contractions in partially ordered metric spaces, Fixed Point Theory and Applications 2012, 2012:44, doi: 10.1186/1687-1812-2012-44] and Binayak S. Choudhury, Erdal Karapinar and Amaresh Kundu [B. Choudhury, E. Karapinar, A. Kundu, Tripled coincidence point theorems for nonlinear contractions in partially ordered metric spaces, International Journal of Mathematics and Mathematical Sciences,2012, in press]. Examples to support our new results are given.

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References

  1. M. Abbas, M. Ali Khan and S. Radenović, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Applied Mathematics and Computation 217 (2010) 195-202.
  2. M. Abbas, T. Nazir, S. Romaguera, Fixed point results for generalized cyclic contraction mappings in partial metric spaces, Rev. R. Acad.Cienc.Exactas Fis.Nat. Ser. A Mat. RACSAM. doi: 10.1007/s13398-011-0051-5.
  3. T. Abdeljawad, E. Karapinar, K. Tas, Existence and uniqueness of a common fixed point on partial metric spaces, Appl. Math. Lett. 24 (2011) 1900-1904.
  4. I. Altun, S. Romaguera, Characterizations of partial metric completeness in terms of weakly contractive mappings having fixed point, Appl. Anal. Discrete Math. (to appear) DOI: 10.2298/AADM120322009A
  5. H. Aydi, E. Karapinar, M. Postolache, Tripled coincidence point theorems for weak ïª-contractions in partially ordered metric spaces, Fixed Point Theory and Applications 2012, 2012:44, doi: 10.1186/1687-1812-2012-44.
  6. H. Aydi, E. Karapinar, B. Samet, Remarks on some recent fixed point theorems, Fixed Point Theory and Applications 2012, 2012:76, doi: 10.1186/1687-1812-2012-76
  7. M. Bakutin, R. Kopperman, S. Matthews, H. Pajoohesh, Partial metric spaces, Am. Math. Monthly 116 (2009) 708-718.
  8. V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Analysis 74 (2011) 4889-4897.
  9. V. Berinde, M. Borcut, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Applied Mathematics and Computation 218 (2012) 5929-5936.
  10. T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered cone metric spaces and applications, Nonlinear Analysis 65 (2006) 825-832.
  11. A. G. Bin Ahmad, Z. M. Fadail, V. ĆojbaÅ¡ić Rajić, S. Radenović, Nonlinear contractions in 0-complete partial metric spaces, Abstract and Applied Analysis, Vol. 2012, article ID 451239, 12 pages, doi:10.1155/2012/451239.
  12. M. Borcut, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Applied Mathematics and Computation 218 (2012) 7339-7346.
  13. B. S. Coudhury, E. Karapinar and A. Kundu, Tripled coincidence point theorems for nonlinear contractions in partially ordered metric spaces, International Journal of Mathematics and Mathematical Sciences, 2012, in press.
  14. B. S. Choudhury and A.Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Analysis 8 (2010) 2524-2531.
  15. Z. Golubović, Z. Kadelburg, S. Radenović , Coupled coincidence points of mappings in ordered partial metric spaces, Abstract and Applied Analysis, Vol. 2012, Article ID 192581, 18 pages, doi: 10.1155/2012/192581.
  16. N. Hussain, Z. Kadelburg, S. Radenović, Comparison functions and fixed point results in partial metric spaces, Abstract and Applied Analysis, Vol. 2012, Article ID 605781, 15 pages, doi:10.1155/2012/605781
  17. D. Ilić, V. Pavlović and V. RakoÄević, Some new extensions of Banach's contractions principle in partial metric spaces, Appl. Math. Lett. 24 (2011) 1326-1330.
  18. M. Jleli, V. ĆojbaÅ¡ić Rajić, B. Samet and C. Vetro, Fixed point theorems on ordered metric spaces and applications to nonlinear beam equations, Journal of Fixed Point Theory and its Applications (2012), doi: 10.1007/s11784-012-0081-4.
  19. Z. Kadelburg, H. K. Nashine, S. Radenović, Fixed point results under various contractive conditions in partial metric spaces, Rev. R. Acad.Cienc.Exactas Fis.Nat. Ser. AMat. RACSAM. doi: 10.1007/s13398-012-0066-6.
  20. V. Lakshmikantham and Lj. Ćirić, Coupled fixed point theorems for nonlinear contractions in partial ordered metric space, Nonlinear Analysis 70 (2009) 4341-4349.
  21. N. V. Luong and N. X. Thuan, Coupled fixed point theorems in partially ordered metric spaces, Bulletin of Mathematical Analysis and Applications 4 (2010) 16-24.
  22. N. V. Luong and N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Analysis, 74(2011) 983-992.
  23. S. G. Matthews, Partial metric topology, Research Report 212. Dept. of Computer Science, University of Warwick, 1992.
  24. S. G. Matthews, Partial metric topology, Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci. 728 (1994), 183-197.
  25. S. Oltra, S. Romaguera, E. A. Saanchez-Perez, Bicompleting weightable quasi-metric spaces and partial metric spaces, Rend. Circ.Mat. Palermo 51(2002) 151-162.
  26. S. Oltra and O. Valer, Banach's fixed point theorem for partial metric spaces, Rend. Istit. Math. Univ. Trieste 36 (2004) 17-26.
  27. S. Radenović, Z. Kadelburg, D. Jandrlić, A. Jandrlić, Some results on weakly contractive maps, Bulletin of the Iranian Mathematical Society (2011), available online since 30 March 2011.
  28. S. Romaguera, Fixed point theorems for generalized contractions on partial metric spaces, Topol. Appl. 159 (2012) 194-199.
  29. B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler Contraction in partially ordered metric spaces, Nonlinear Analysis 72 (2010) 4508-4517.