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

Yıl 2016, Cilt: 29 Sayı: 1, 149 - 158, 21.03.2016

Muzeyyen Sangurlu Arslan Ansari Duran Turkoglu

Öz

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].

Anahtar Kelimeler

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

Kaynakça

• 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.
• 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.
• 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.
• Ansari, A. H. Note on ϕ-ψ- contractive type mappings and related fixed point, The 2nd
• Regional Conference on Mathematics And Applications, Payame Noor University, (2014) 377-380
• 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.
• Agarwal, R.P., El-Gebeily, M.A. and Regan, D.O. Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008) 1-8.
• 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.
• 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.
• 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.
• Luong, N.V. and Thuan, N.X. Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983.992.
• Berinde, V. Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011) 7347.7355.
• 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.
• 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.
• Samet, B. Coupled fixed point theorems for a generalized Meir.Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010) 4508.4517.
• Bhaskar, T.G. and Lakshmikantham, V. Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65 (2006) 1379-1393.
• 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.
• 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. *
• Radenovi´c S. and Kadelburg, Z. Generalized weak contractions in partially ordered metric spaces, Comput. Math. Appl. 60 (2010) 1776.1783.
• Banach, S. Sur les opérations dans les ensembles abstraits et leur application aux equations intégrales, Fund. Math. 3 (1922) 133-181.
• 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.
• 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.
• Sintunavarat, W. and Kumam, P. Coupled best proximity point theorem in metric spaces, Fixed Point Theory and Applications 2012, 2012:93.
• Sintunavarat, W. and Kumam, P. Coupled coincidence and coupled common fixed point theorems in partially ordered metric spaces, Thai Journal of Mathematics 2012 (inpress).
• 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.
• 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
• di Palermo, 61 (2012) 361-383.
• 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.
• 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.
• 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.
• 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.
• 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.
• 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.