Coupled fixed point theorems for compatible mappings in partially ordered $G$-metric spaces
Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 2, p. 130-141.

Voir la notice de l'article provenant de la source International Scientific Research Publications

In this paper, we prove coupled coincidence and coupled common fixed point theorems for compatible mappings in partially ordered G-metric spaces. The results on fixed point theorems are generalizations of some existing results. We also give an example to support our results.
DOI : 10.22436/jnsa.008.02.05
Classification : 47H10, 54H25
Keywords: partially ordered set, couple coincidence point, coupled fixed point, compatible mappings, G-metric space.

Chen, Jianhua 1 ; Huang, Xianjiu 1

1 Department of Mathematics, Nanchang University, Nanchang, 330031, P. R. China
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Chen, Jianhua; Huang, Xianjiu. Coupled fixed point theorems for compatible mappings in partially ordered \(G\)-metric spaces. Journal of nonlinear sciences and its applications, Tome 8 (2015) no. 2, p. 130-141. doi : 10.22436/jnsa.008.02.05. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.008.02.05/

[1] Abbas, M.; Khan, M. A.; Radenović, S. Common coupled fixed point theorem in cone metric space for \(w^*\)-compatible mappings , Appl. Math. Comput., Volume 217 (2010), pp. 195-202

[2] Agarwal, R. P.; El-Gebeily, M. A.; O'Regan, D. Generalized contractions in partially ordered metric spaces, Appl. Anal., Volume 87 (2008), pp. 109-116

[3] Aydi, H.; Damjanović, B.; Samet, B.; Shatanawi, W. Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces , Math. Comput. Modelling, Volume 54 (2011), pp. 2443-2450

[4] Bhaskar, T. G.; V. Lakshmikantham Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., Volume 65 (2006), pp. 1379-1393

[5] Choudhury, B. S.; Kundu, A. A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal., Volume 73 (2010), pp. 2524-2531

[6] Choudhury, B. S.; Maity, P. Coupled fixed point results in generalized metric spaces, Math. Comput. Modelling, Volume 54 (2011), pp. 73-79

[7] Chugh, R.; Kadian, T.; Rani, A.; Rhoades, B. E. Property P in G-metric spaces, Fixed Point Theory Appl., Volume 2010 (2010), pp. 1-12

[8] Ćirić, Lj.; Cakić, N.; Rajović, M.; Ume, J. S. Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl., Volume 2008 (2008), pp. 1-11

[9] Ćirić, Lj.; Mihet, D.; Saadati, R. Monotone generalized contractions in partially ordered probabilistic metric spaces, Topology Appl., Volume 156(17) (2009), pp. 2838-2844

[10] Jain, M.; Tas, K.; Rhoades, B. E.; Gupta, N. Coupled fixed point theorems for generalized symmetric contractions in partially ordered metric spaces and applications, J. Comput. Anal. Appl., Volume 16 (2014), pp. 438-454

[11] Karapinar, E.; Kumam, P.; Merhan, I. Coupled fixed point theorems on partially ordered G-metric spaces, Fixed Point Theory Appl., Volume 2012 (2012), pp. 1-13

[12] Lakshmikantham, V.; Ćirić, Lj. Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., Volume 70 (2009), pp. 4341-4349

[13] Luong, N. V.; N. X. Thuan Coupled fixed point theorems in partially ordered G-metric spaces, Math. Comput. Modelling, Volume 55 (2012), pp. 1601-1609

[14] Mohiuddine, S. A.; Alotaibi, A. Coupled coincidence point theorems for compatible mappings in partially ordered intuitionistic generalized fuzzy metric spaces, Fixed Point Theory Appl., Volume 2013 (2013), pp. 1-18

[15] Mustafa, Z.; Sims, B. A new approach to generalized metric spaces, J. Nonlinear Convex Anal., Volume 7 (2006), pp. 289-297

[16] Mustafa, Z.; Obiedat, H.; Awawdeh, F. Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., Volume 2008 (2008), pp. 1-12

[17] Mustafa, Z.; Hatanawi, W.; Bataineh, M. Existence of fixed point results in G-metric spaces, Int. J. Math. Math. Sci., Volume 2009 (2009), pp. 1-10

[18] Mustafa, Z.; Sims, B. Fixed point theorems for contractive mappings in complete G-metric spaces, Fixed Point Theory Appl., Volume 2009 (2009), pp. 1-10

[19] Nashine, H. K.; B. Samet Fixed point results for mappings satisfying (\(\psi,\varphi\))-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., Volume 74 (2011), pp. 2201-2209

[20] Nashine, H. K. Coupled common fixed point results in ordered G-metric spaces, J. Nonlinear Sci. Appl., Volume 5 (2012), pp. 1-13

[21] B. Samet Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., Volume 72 (2010), pp. 4508-4517

[22] Shatanawi, W. Partially ordered cone metric spaces and coupled fixed point results, Comput. Math. Appl., Volume 60 (2010), pp. 2508-2515

[23] Shatanawi, W. Fixed point theory for contractive mappings satisfying \(\Phi\)-maps in G-metric spaces, Fixed Point Theory Appl., Volume 2010 (2010), pp. 1-9

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