DOI QR코드

DOI QR Code

COUPLED COINCIDENCE POINT RESULTS WITH MAPPINGS SATISFYING RATIONAL INEQUALITY IN PARTIALLY ORDERED METRIC SPACES

  • Received : 2015.04.21
  • Accepted : 2017.12.29
  • Published : 2019.01.30

Abstract

In this paper we prove certain coupled coincidence point and coupled common fixed point results in partially ordered metric spaces for a pair of compatible mappings which satisfy certain rational inequality. The results are supported with two examples.

Keywords

References

  1. M. Abbas, C.V. Rajic, T. Nazir and S. Radenovic, Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces, Afrika Mat. 26 (2015), 17-30. https://doi.org/10.1007/s13370-013-0185-z
  2. G.V.R. Babu and P. Subhashini, Coupled common fixed points for a pair of compatible maps satisfying geraghty contraction in partially ordered metric spaces, International Journal of Mathematics and Scientific Computing 2 (2012), 41-48.
  3. G.V.R. Babu and M.V.R. Kameswari, Coupled fixed points for generalized contractive maps with rational expressions in partially ordered metric spaces, Journal of Advanced Research in Pure Mathematics 6 (2014), 43-57. https://doi.org/10.5373/jarpm.1686.020513
  4. S. Bhatt, S. Chaukiyal and R.C. Dimri, Common fixed point of mappings satisfying rational inequality in complex valued metric space, Int. J. Pure Appl. Math. 73 (2011), 159-164.
  5. S. Chandok and J.K. Kim, Fixed point theorem in ordered metric spaces for generalized contractions mappings satisfying rational type expressions, J. Nonlinear Functional Anal. Appl. 17 (2012), 301-306.
  6. S. Chandok, B.S. Choudhury and N. Metiya, Fixed point results in ordered metric spaces for rational type expressions with auxiliary functions, J. Egyptian Math. Soc. 23 (2015), 95-101. https://doi.org/10.1016/j.joems.2014.02.002
  7. 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. https://doi.org/10.1016/j.na.2010.06.025
  8. B.S. Choudhury, N. Metiya and A. Kundu, Coupled coincidence point theorems in ordered metric spaces, Ann. Univ. Ferrara 57 (2011), 1-16. https://doi.org/10.1007/s11565-011-0117-5
  9. B.S. Choudhury, N. Metiya and M. Postolache, A generalized weak contraction principle with applications to coupled coincidence point problems, Fixed Point Theory Appl. 2013 (2013) :152. https://doi.org/10.1186/1687-1812-2013-152
  10. B.S. Choudhury and N. Metiya, Fixed point results for mapping satisfying rational inequality in complex valued metric spaces, J. Adv. Math. Stud. 7 (2014), 79-89.
  11. L. Ciric and V. Lakshmikantham, Coupled random fixed point theorems in partially ordered metric spaces, Stoch. Anal. 27 (2009), 1246-1259. https://doi.org/10.1080/07362990903259967
  12. B.K. Dass and S. Gupta, An extension of Banach contraction principle through rational expressions, Inidan J. Pure Appl. Math. 6 (1975), 1455-1458.
  13. T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379-1393. https://doi.org/10.1016/j.na.2005.10.017
  14. D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. 11 (1987), 623-632. https://doi.org/10.1016/0362-546X(87)90077-0
  15. J. Harjani, B. Lopez and K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal. 74 (2011), 1749-1760. https://doi.org/10.1016/j.na.2010.10.047
  16. D.S. Jaggi and B.K. Das, An extension of Banach's fixed point theorem through rational expression, Bull. Cal. Math. Soc. 72 (1980), 261-264.
  17. E. Karapinar, Couple xed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl. 59 (2010), 3656-3668. https://doi.org/10.1016/j.camwa.2010.03.062
  18. V. Lakshmikantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341-4349. https://doi.org/10.1016/j.na.2008.09.020
  19. N.V. Luong and N.X. Thuan, Coupled fixed point theorem in partially ordered metric space, Bull. Math. Anal. Appl. 2 (2010), 16-24.
  20. H.K. Nashine, B.S. Choudhury and N. Metiya, Coupled coincidence point theorems in partially ordered metric spaces, Thai J. Math. 12 (2014), 665-685.
  21. W. Shatanawi, Partially ordered cone metric spaces and coupled fixed point results, Comput. Math. Appl. 60 (2010), 2508-2515. https://doi.org/10.1016/j.camwa.2010.08.074