Coupled Fixed Point Theorems For Mixed G-Monotone Mappings In Partially Ordered Metric Spaces Via New Functions

Abstract

In this paper, we prove some coupled coincidence point results for mixed g-monotone mappings in partially ordered metric spaces via new functions. The main results of this paper are generalizations of the main results of Luong and Thuan [ N.V. Luong, N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983992].

Keywords

• Coupled fixed point
• C-class function
• Partially Ordered Metric Space

References

1. Aydi, H., Karapinar, E. and Shatanawi, W. Coupled fixed point results for (ψ-ϕ)-weakly contractive condition in ordered partial metric spaces, Computers and Mathematics with Appl. 62 (2011) 4449-4460.
2. Altun, I. and Simsek, H. Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl. 2010 (2010) 17 pages. Article ID 621469.
3. Harjani, J. and Sadarangani, K. Generalized contractions in partially ordered metric spaces and applications to ordinary diferential equations, Nonlinear Anal. TMA 72 (2010) 1188-1197.
4. Ansari, A. H. Note on ϕ-ψ- contractive type mappings and related fixed point, The 2nd
5. Regional Conference on Mathematics And Applications, Payame Noor University, (2014) 377-380
6. Samet, B. Coupled fixed point theorems for a generalized Meir-Keler contraction in partially ordered metric spaces, Nonlinear Anal. TMA (2010) doi: 10.1016/j.na.2010.02.026.
7. Agarwal, R.P., El-Gebeily, M.A. and Regan, D.O. Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008) 1-8.
8. Nieto, J.J. and Rodriquez-Lopez, R. Contractive mapping theorems in partially ordered sets and applications to ordinary diferential aquation, Order 22 (2005) 223-239.

9. Nieto, J.J. and Rodriquez-Lopez, R. Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary diferential aquations, Acta Math. Sin. (Engl. Ser.) 23 (12) (2007) 2205- 2212.
10. Ran, A.C.M. and Reurings, M.C.B. A. Fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1453-1443.
11. Luong, N.V. and Thuan, N.X. Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983.992.
12. Berinde, V. Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 7347.7355.
13. Choudhury, B.S. and Kundu, A. A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal. 73 (2010) 2524.2531.
14. Nashine, H.K. and Shatanawi, W. Coupled common fixed point theorems for pair of commuting mappings in partially ordered complete metric spaces, Comput. Math. Appl. 62 (2011) 1984.1993.
15. Samet, B. Coupled fixed point theorems for a generalized Meir.Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010) 4508.4517.
16. Bhaskar, T.G. and Lakshmikantham, V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65 (2006) 1379-1393.
17. Lakshmikantham, V. and C´ iric, Lj. B. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis (2008) doi: 10.1016/j.na.2008.09.020.
18. Nashine, H. K., Kadelburg Z. and Radenovi´c, S. Coupled common fixed point theorems for compatible mappings in ordered cone metric spaces, Applied Mathematics and Computation 218 (2012) 5422-5432. *
19. Radenovi´c S. and Kadelburg, Z. Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010) 1776.1783.
20. Banach, S. Sur les opérations dans les ensembles abstraits et leur application aux equations intégrales, Fund. Math. 3 (1922) 133-181.
21. Abbas, M., Sintunavarat, W. and Kumam, P. Coupled fixed point of generalized contractive mappings on partially ordered G-metric spaces, Fixed Point Theory and Applications 2012, 2012:31.
22. Sintunavarat, W., Cho, Y. J. and Kumam, P. Coupled fixed point theorems for weak contraction mapping under F-invariant set, Abstr. Appl. Anal. Volume 2012, Article ID 324874, 15 pages,2012.
23. Sintunavarat, W. and Kumam, P. Coupled best proximity point theorem in metric spaces, Fixed Point Theory and Applications 2012, 2012:93.
24. Sintunavarat, W. and Kumam, P. Coupled coincidence and coupled common fixed point theorems in partially ordered metric spaces, Thai Journal of Mathematics 2012 (inpress).
25. Sintunavarat, W., Cho, Y. J. and Kumam, P. Coupled fixed point theorems for contraction mapping induced by cone ball-metric in partially ordered spaces, Fixed Point Theory and Applications 2012, 2012:128.
26. Sintunavarat, W., Petru sel, A. and Kumam, P. Common coupled fixed point theorems for w - compatible mappings without mixed monotone property, Rendiconti del Circolo Matematico
27. di Palermo, 61 (2012) 361-383.
28. Sintunavarat, W., Kumam, P. and Cho, Y. J. Coupled fixed point theorems for nonlinear contractions without mixed monotone property, Fixed Point Theory and Applications 2012, 2012:170.
29. Karapınar, E., Kumam P. and Sintunavarat, W. Coupled fixed point theorems in cone metric spaces with a c-distance and applications, Fixed Point Theory and Applications 2012, 2012:194.
30. Sintunavarat, W., Radenovic, S., Golubovic, Z. and Kumam, P. Coupled fixed point theorems for F-invariant set, Appl. Math. Inf. Sci. 7(1) (2013) 247-255.
31. Haghi, RH, Rezapour, Sh, Shahzad, N, Some fixed point generalizations are not real generalizations, Nonlinear Anal. 74,1799-1803 (2011). doi:10.1016/j.na.2010, 10.052.
32. Sintunavarat, W., Cho, Y.J. and Kumam, P. Coupled coincidence point theorems for contractions without commutative condition in intuitionistic fuzzy normed spaces, Fixed Point Theory and Applications 2011, 2011:81.
33. Turkoglu, D. and Sangurlu, M. Coupled fixed point theorems for mixed g-monotone mappings in partially ordered metric spaces, Fixed Point Theory and Applications 2013, 2013:348.