East Asian mathematical journal

The Youngnam Mathematical Society (영남수학회)
권호 표지
DOI QR코드

DOI QR Code

COUPLED FIXED POINT THEOREMS FOR RATIONAL INEQUALITY IN GENERALIZED METRIC SPACES

  • Singh, Deepak (Department of Applied Sciences, NITTTR) ;
  • Tomar, Surjeet Singh (Department of Mathematics, Jai Narayan College of Technology) ;
  • Rathore, M.S. (Department of Mathematics, Chandra Shekhar Azad Govt. P.G. College) ;
  • Chauhan, Varsha (Department of Mathematics, NRI Institute of Research and Technology)
  • Received : 2013.12.19
  • Accepted : 2014.12.03
  • Published : 2015.01.31
Download PDF
⟨ Previous Next ⟩

Abstract

In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G-metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.

Keywords

References

  1. R. P. Agarwal, M. A. El-Gebeily and D. O'Regan, Generalized contractions in partially ordered metric spaces, Applicable Analysis 87 (2008), 109-116. https://doi.org/10.1080/00036810701556151
  2. A. Amini-Harandi and H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Analysis, 72 (2010), 2238-2242. https://doi.org/10.1016/j.na.2009.10.023
  3. H. Aydi, B. Damjanovic, B. Samet and W. Shatanawi, Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, 10.1016/j.mcm.2011.05.059.
  4. T. G. 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
  5. B. S. Choudhury and P. Maity, Coupled fixed point results in generalized metric spaces, Math. Comput.Mod.(2011), doi:10.1016/j.mcm.2011.01.036.
  6. B.S. Choudhury, A. Kundu, Coupled fixed point results in generalized metric spaces, Mathematical and Computer Modelling. 54(2011), 73-79. https://doi.org/10.1016/j.mcm.2011.01.036
  7. Lj. B. Ciric, N. Cakic, M. Rajovic and J. S. Ume, Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl. 2008(2008), Article ID 131294, 11 pages.
  8. Lj. B. Ciric, D. Mihet and R. Saadati, Monotone generalized contractions in partially ordered probabilistic metric spaces, Topology and its Applications 156(2009), 2838-2844. https://doi.org/10.1016/j.topol.2009.08.029
  9. D. Guo and V. Lakshmikantham, Coupled fixed point of nonlinear operators with applications, Nonlinear Anal. 11(1987), 623-632. https://doi.org/10.1016/0362-546X(87)90077-0
  10. Z. Kadelburg, M. Pavlovic and S. Radenovic, Common fixed point theorems for ordered contractions and quasi contractions in ordered cone metric spaces, Comp. Math. Appl., 59(2010), 3148-3159. https://doi.org/10.1016/j.camwa.2010.02.039
  11. V.Lakshmikantham, Lj.B.Ciric: Coupled fixed point theorems for nonlinear contraction-sin partially ordered metric space, Nonlinear Anal. 70 (2009) 4341-4349. https://doi.org/10.1016/j.na.2008.09.020
  12. Z. Mustafa and B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal. 7(2)(2006), 289-297.
  13. Z. Mustafa, H. Obiedat and F. Awawdeh, Some of fixed point theorem for map-ping on complete G-metric spaces, Fixed Point Theory Appl., 2008(2008), Article ID 189870,page 12.
  14. Z. Mustafa, W. Shatanawi and M. Bataineh, Fixed point theorems on uncomplete G-metric spaces, J. Math. Stat. 4(4)(2008), 196-201. https://doi.org/10.3844/jmssp.2007.196.200
  15. Z. Mustafa, W. Shatanawi and M. Bataineh, Existence of fixed point result in G-metric spaces, Int. J. Math. Math. Sci. 2009(2009), page 10, Article ID 283028.
  16. Z. Mustafa and B. Sims, Fixed point theorems for contractive mappings in complete G-metric space, Fixed Point Theory Appl. 2009(2009), page 10, Article ID 917175.
  17. Z. Mustafa, B. Sims, Some remarks concerning D-metric spaces. Proceedings of the International Conference on Fixed Point Theory and Applications, Valencia, Spain. 189-198 (2003)
  18. J.J. Nieto, R.R. Lopez, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239. https://doi.org/10.1007/s11083-005-9018-5
  19. A.C.M. Ran, 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. https://doi.org/10.1090/S0002-9939-03-07220-4
  20. R. Saadati, S. M. Vaezpour, P. Vetro and B. E. Rhoades, Fixed point theorems in generalized partially ordered G-metric spaces, Math. Comput. Modelling 52(2010), 797-801. https://doi.org/10.1016/j.mcm.2010.05.009