Some Coupled Coincidence Points Results of Monotone Mappings in Partially Ordered Metric Spaces

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Stojan Radenovic, Some Coupled Coincidence Points Results of Monotone Mappings in Partially Ordered Metric Spaces, Int. J. Anal. Appl., 5 (2) (2014), 174-184.

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Stojan Radenovic

Abstract

In this paper, we introduce the concepts of a monotone mappings and monotone mapping with respect to other mapping to obtain some coupled coincidence point results in partially ordered metric spaces. Our results generalize, extend and complement various comparable results in the existing literature.

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References

  1. M. Abbas, M. A. Khan and S. Radenovi ´c, Common coupled fixed point theorem in cone metric space for w-compatible mappings, Appl. Math.Comput. 217 (2010) 195-202.
  2. M. Abbas, T. Nazir, S. Radenovi ´c, Common coupled fixed points of generalized contractive mappings in partially ordered metric spaces, Positivity (2013) 17:1021-1041.
  3. R. P. Agarval, M. A. El-Gebeily and D. O'Regan, Generalized contractions in partially ordered metric spaces, Applicable Analysis 87 (1) (2008) 109-116.
  4. I. Altun and H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl. Volume 2010, Article ID 621469.
  5. T. G. Bhashkar and V. Lakshmikantham, Fixed point theorems in partially ordered cone metric spaces and applications, Nonlinear Anal. 65 (7) (2006) 825-832.
  6. B. S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal. 73 (2010) 2524-2531.
  7. H. S. Ding, Lu Li and S. Radenovi ´c, Coupled coincidence point theorems for generalized nonlinear contraction in partially ordered metric spaces, Fixed Point Theory Appl. 2012, 2012:96.
  8. D. Guo, V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. TMA 11 (1987) 623-632.
  9. A. A. Harandi and H. Emami, A fixed point theorem for contractive type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Anal. TMA 72 (2010) 2238-2242.
  10. J. Harjani and K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. 71 (2009) 3403-3410.
  11. E. Karapinar, Coupled fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl. 59 (2010) 3656-3668.
  12. M. Borcut, Tripled fixed point theorems for monotone mappings in partially ordered metric spaces, Carpanthian J. Math. 28 (2012), No. 2, 207-214.
  13. J. J. Nieto and R. R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239.
  14. V.I. Opoitsev, Heterogenic and combined-concave operators, Syber. Math. J. 16 (1975) 781- 792 (in Russian).
  15. V.I. Opoitsev, Dynamics of collective behavior. III. Heterogenic systems. Avtomat. i Telemekh. 36 (1975), 124-138 (in Russian).
  16. V.I. Opoitsev, T.A. Khurodze, Nonlinear operators in space with a cone. Tbilis. Gos. Univ. Tbilisi (1984) 271 (in Russian).
  17. S. Radenovi ´c and Z. Kadelburg, Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010) 1776-1783.
  18. S. Radenovi ´c, Remarks on some coupled coincidence point results in partially ordered metric spaces, Arab J. Math. Sci. 20 (1) (2014), 29-39.
  19. A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443.
  20. D. O'Regan and A. Petrusel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal.Appl., 341 (2008) 1241-1252.