DOI QR코드

DOI QR Code

COUPLED FIXED POINTS FOR MIXED g-MONOTONE UNDER RATIONAL CONTRACTIVE EXPRESSIONS IN PARTIALLY ORDERED METRIC SPACES

  • Nashine, Hemant Kumar (Department of Mathematics, Amity School of Applied Sciences, Amity University) ;
  • Gupta, Anita (Department of Mathematics, Dr C.V.Raman University)
  • 투고 : 2014.09.25
  • 심사 : 2016.09.30
  • 발행 : 2016.09.30

초록

We propose coupled fixed point theorems for maps satisfying contractive conditions involving a rational expression in the setting of partially ordered metric spaces. We also present a result on the existence and uniqueness of coupled fixed points. In particular, it is shown that the results existing in the literature are extend, generalized, unify and improved by using mixed monotone property. Given to support the useability of our results, and to distinguish them from the known ones.

키워드

참고문헌

  1. V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. TMA 74 (2011), 7347-7355. https://doi.org/10.1016/j.na.2011.07.053
  2. T. G. Bhaskar, and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006), 1379-1393. https://doi.org/10.1016/j.na.2005.10.017
  3. D. Guo, and V. Lakshmikantham, Coupled fixed points of nonlinear operators with ap-plications, Nonlinear Anal. TMA 11 (1987), 623-632. https://doi.org/10.1016/0362-546X(87)90077-0
  4. H. S. Ding, and L. Li, Coupled fixed point theorems in partially ordered cone metric spaces, Filomat 25 (2011), no. 2, 137-149. https://doi.org/10.2298/FIL1102137D
  5. J. Harjani, and K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. TMA 71 (2008), 3403-3410.
  6. J. Harjani, and K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal. TMA 72 (2010), 1188-1197. https://doi.org/10.1016/j.na.2009.08.003
  7. V. Lakshmikantham, and Lj. B. Ciric, Coupled fixed point theorems for nonlinear con-tractions in partially ordered metric spaces, Nonlinear Anal. TMA 70 (2009), 4341-4349. https://doi.org/10.1016/j.na.2008.09.020
  8. N. V. Luong, and N. X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. TMA 74 (2011), 983-992.
  9. N. V. Luong, N. X. Thuan, Coupled fixed point theorems for mixed monotone mappings and an application to integral equations, Comput. Math. Appl. 62 (2011), 4238-4248. https://doi.org/10.1016/j.camwa.2011.10.011
  10. H. K. Nashine, Z. Kadelburg, and S. Radenovic, Coupled common fixed point theorems for w*-compatible mappings in ordered cone metric spaces, Appl. Math. Comput. 218 (2011), 5422-5432.
  11. H. K. Nashine, and W. Shatanawi, Coupled common fixed point theorems for pair of commuting mappings in partially ordered complete metric spaces, Comput. Math. Appl. 62 (2011), 1984-1993. https://doi.org/10.1016/j.camwa.2011.06.042
  12. 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. https://doi.org/10.1007/s11083-005-9018-5
  13. J. J. Nieto, and R.R. Lopez, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sinica, Engl. Ser. 23 (2007), 2205-2212. https://doi.org/10.1007/s10114-005-0769-0
  14. A. C. M. Ran, and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004), 1435-1443. https://doi.org/10.1090/S0002-9939-03-07220-4
  15. B. E. Rhoades, Proving fixed point theorems using general principles, Indian J. Pure Appl. Math. 27 (1996), 741-770.
  16. B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. TMA 72 (2010), 4508-4517. https://doi.org/10.1016/j.na.2010.02.026
  17. B. Samet, and H. Yazidi, Coupled fixed point theorems in partially ordered ${\varepsilon}$-chainable metric spaces, J. Math. Comput. Sci. 1 (2010), 142-151. https://doi.org/10.22436/jmcs.001.03.02
  18. Y. Wu, New fixed point theorems and applications of mixed monotone operator, J. Math. Anal. Appl. 341(2) (2008), 883-893. https://doi.org/10.1016/j.jmaa.2007.10.063
  19. Y. Wu, and Z. Liang, Existence and uniqueness of fixed points for mixed monotone operators with applications, Nonlinear Anal. TMA 65 (2006), 1913-1924. https://doi.org/10.1016/j.na.2005.10.045
  20. B. S. Choudhury, and A. Kundu, A coupled coincidence point results in partially ordered metric spaces for compatible mappings, Nonlinear Anal. 73 (2010), 2534-2531.
  21. H. K. Nashine, B. Samet, and C. Vetro, Coupled coincidence point for compatible map-pings satisfying mixed monotone property, J. Nonlinear Sci. and Appl. 5 (2012), 104-114. https://doi.org/10.22436/jnsa.005.02.04
  22. W. Shatanawi, B. Samet, and M. Abbas, Coupled fixed point for mixed monotone map-ping in ordered partial metric spaces, J. Math. Comput. Modelling 55 (2012), 680-687. https://doi.org/10.1016/j.mcm.2011.08.042
  23. B. S. Choudhury, N. Meitya, and P. Das, A coupled common fixed point theorem for a family of mappings, Nonlinear Anal. 18 (2013), no. 1, 14-26.
  24. H. K. Nashine, and Z. Kadelburg, Partially ordered metric spaces, Rational Contractive expressions and coupled fixed points, 17(2012), no. 4, 471-489.