Geodesic
Coupled common fixed point results in ordered G-metric spaces
Nashine, Hemant Kumar1
1 Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Naradha, Mandir Hasaud, Raipur-492101 (Chhattisgarh), India
Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 1, p. 1-13.

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

In the present paper, we prove coupled common fixed point theorems in the setting of a partially ordered G-metric space in the sense of Z. Mustafa and B. Sims. Examples are given to support the usability of our results and to distinguish them from the existing ones.
DOI : 10.22436/jnsa.005.01.01
Classification : 54H25, 47H10
Keywords: Coupled fixed point, Coupled common fixed point, G-metric space, Mixed g-monotone property, Partial order, Commuting maps.

Nashine, Hemant Kumar 1

1 Department of Mathematics, Disha Institute of Management and Technology, Satya Vihar, Vidhansabha-Chandrakhuri Marg, Naradha, Mandir Hasaud, Raipur-492101 (Chhattisgarh), India 
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Nashine, Hemant Kumar. Coupled common fixed point results in ordered G-metric spaces. Journal of nonlinear sciences and its applications, Tome 5 (2012) no. 1, p. 1-13. doi : 10.22436/jnsa.005.01.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.005.01.01/

[1] Abbas, M.; Rhoades, B. E. Common fixed point results for noncommuting mappings without continuity in generalised metric spaces, Appl. Math. Comput. , Volume 215 (2009), pp. 262-269

[2] Abbas, M.; Nazir, Talat; Stojan Radenovic Some periodic point results in generalized metric spaces, Appl. Math. Comput., Volume 217 (2010), pp. 4094-4099

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

[4] Altun, I. Some fixed point theorems for single and multi valued mappings on ordered nonarchimedean fuzzy metric spaces, Iranian J. Fuzzy Systems , Volume 7 (2010), pp. 91-96

[5] Altun, I.; Mihet, D. Ordered non-archimedean fuzzy metric spaces and some fixed point results, Fixed Point Theory Appl. , Volume 2010 (2010), pp. 1-11

[6] Altun, I.; Simsek, H. Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl. , Volume 2010 (2010), pp. 1-17

[7] Amini-Harandi, A.; Emami, H. A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations, Nonlinear Analysis, Volume 72 (2010), pp. 2238-2242

[8] Aydi, H.; Damjanović, B.; Samet, B.; W. Shatanawi Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, 10.1016/j.mcm.2011.05.059. , , 2011

[9] Beg, I.; Butt, A. R. Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal. , Volume 71 (2009), pp. 3699-3704

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

[11] Cabada, A.; Nieto, J. J. Fixed points and approximate solutions for nonlinear operator equations, J. Comput. Appl. Math., Volume 113(1-2) (2000), pp. 17-25

[12] Caballero, J.; Harjani, J.; Sadarangani, K. Contractive-like mapping principles in ordered metric spaces and application to ordinary differential equations , Fixed Point Theory Appl. , Volume 2010 (2010), pp. 1-14

[13] Choudhury, B. S.; Maity, P. Coupled fixed point results in generalized metric spaces, Math. Comput. Mod. , doi:10.1016/j.mcm.2011.01.036. , 2011

[14] 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

[15] Ćirić, Lj.; Lakshmikantham, V. Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces, Stoch. Anal. Appl. , Volume 27(6) (2009), pp. 1246-1259

[16] Ćirić, Lj. B.; 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

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

[18] Dhage, B. C. Generalized metric spaces and mappings with fixed point, Bull. Calcutta Math. Soc. , Volume 84 (1992), pp. 329-336

[19] Guo, D.; Lakshmikantham, V. Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. , Volume 11 (1987), pp. 623-632

[20] Harjani, J.; K. Sadarangani Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal. , Volume 71 (2009), pp. 3403-3410

[21] Harjani, J.; K. Sadarangani Generalized contractions in partially ordered metric spaces and applications to ordianry differential equations, Nonlinear Anal., Volume 72 (2010), pp. 1188-1197

[22] Harjani, J.; López, B.; K. Sadarangani A fixed point theorem for mappings satisfying a contractive condition of rational type on a partially ordered metric space, Abstract Appl. Anal., Volume 2010 (2010), pp. 1-8

[23] Kadelburg, Z.; Pavlović, M.; Radenović, S. Common fixed point theorems for ordered contractions and quasicontractions in ordered cone metric spaces, Comput. Math. Appl., Volume 59 (2010), pp. 3148-3159

[24] Mustafa, Z. A new structure for generalized metric spaces with applications to fixed point theory, Ph.D. thesis, University of Newcastle, Newcastle, UK, 2005

[25] Mustafa, Z.; Sims, B. Some remarks concerning D-metric spaces, in: Proc. Int. Conf. on Fixed Point Theor. Appl., Valencia, Spain (2003), pp. 189-198

[26] Mustafa, Z.; Sims, B. A new approach to generalized metric spaces, J. Nonlinear Convex Anal. , Volume 7(2) (2006), pp. 289-297

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

[28] Mustafa, Z.; Shatanawi, W.; Bataineh, M. Fixed point theorems on uncomplete G-metric spaces, J. Math. Stat. , Volume 4(4) (2008), pp. 196-201

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

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

[31] Nashine, H. K.; Altun, I. Fixed point theorems for generalized weakly contractive condition in ordered metric spaces, Fixed point Theory and Appl. , Volume 2011 (2011), pp. 1-20

[32] Nashine, H. K.; I. Altun A common fixed point theorem on ordered metric spaces, Bull. Iranian Math. Soc. (2011)

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

[34] Nashine, H. K.; Samet, B.; Kim, J. K. Fixed point results for contractions involving generalized altering distances in ordered metric spaces, Fixed point Theory Appl., doi:10.1186/1687-1812-2011-5. , 2011

[35] Nashine, H. K.; Samet, B.; Vetro, C. Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces, Math. Comput. Modelling , Volume 54 (2011), pp. 712-720

[36] Nashine, H. K.; Shatanawi, W. Coupled common fixed point theorems for pair of commuting mappings in partially ordered complete metric spaces, Comput. Math. Appl., Volume 62 (2011), pp. 1984-1993

[37] Nieto, J. J.; R. Rodríguez-López Contractive mapping theorems in partially ordered sets and applications to ordianry differential equations, Order , Volume 22(3) (2005), pp. 223-239

[38] Ran, A. C. M.; Reurings, M. C. B. A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. , Volume 132 (2004), pp. 1435-1443

[39] Saadati, R.; Vaezpour, S. M.; Vetro, P.; B. E. Rhoades Fixed point theorems in generalized partially ordered G-metric spaces, Math. Comput. Modelling, Volume 52 (2010), pp. 797-801

[40] Shakeri, S.; Ćirić, Lj. B.; R. Saadati Common Fixed Point Theorem in Partially Ordered L-Fuzzy Metric Spaces, Fixed Point Theory Appl. , Volume 2010 (2010), pp. 1-13

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

[42] 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

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

[44] Wu, Y. New fixed point theorems and applications of mixed monotone operator, J. Math. Anal. Appl. , Volume 341(2) (2008), pp. 883-893

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