×

Coupled fixed point results in generalized metric spaces. (English) Zbl 1225.54016

Summary: We establish coupled fixed point theorems in a partially ordered \(G\)-metric space. The results are illustrated by an example.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
65J15 Numerical solutions to equations with nonlinear operators
47H10 Fixed-point theorems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Z. Mustafa, B. Sims, Some remarks concerning \(D\); Z. Mustafa, B. Sims, Some remarks concerning \(D\) · Zbl 1079.54017
[2] Mustafa, Z.; Sims, B., A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7, 2, 289-297 (2006) · Zbl 1111.54025
[3] Mustafa, Z.; Obiedat, H.; Awawdeh, F., Some of fixed point theorem for mapping on complete \(G\)-metric spaces, Fixed Point Theory Appl., 2008 (2008), 12 pp. Article ID 189870 · Zbl 1148.54336
[4] Mustafa, Z.; Shatanawi, W.; Bataineh, M., Fixed point theorems on uncomplete \(G\)-metric spaces, J. Math. Stat., 4, 4, 196-201 (2008)
[5] Mustafa, Z.; Shatanawi, W.; Bataineh, M., Existence of fixed point result in \(G\)-metric spaces, Int. J. Math. Math. Sci., 2009 (2009), 10 pp. Article ID 283028 · Zbl 1179.54066
[6] Mustafa, Z.; Sims, B., Fixed point theorems for contractive mappings in complete \(G\)-metric space, Fixed Point Theory Appl., 2009 (2009), 10 pp. Article ID 917175 · Zbl 1179.54067
[7] Abbas, M.; Rhoades, B. E., Common fixed point results for noncommuting mappings without continuity in generalised metric spaces, Appl. Math. Comput., 215, 262-269 (2009) · Zbl 1185.54037
[8] Saadati, R.; Vaezpour, S. M.; Vetro, P.; Rhoades, B. E., Fixed point theorems in generalized partially ordered \(G\)-metric spaces, Math. Comput. Modelling, 52, 797-801 (2010) · Zbl 1202.54042
[9] Chugh, Renu; Kadian, Tamanna; Rani, Anju; Rhoades, B. E., Property \(P\) in \(G\)-metric spaces, Fixed Point Theory Appl., 2010 (2010), 12 pp. Article ID 401684 · Zbl 1203.54037
[10] Abbas, Mujahid; Nazir, Talat; Radenovic, Stojan, Some periodic point results in generalized metric spaces, Appl. Math. Comput., 217, 8, 4094-4099 (2010) · Zbl 1210.54049
[11] Kamran, T.; Cakić, N., Hybrid tangential property and coincidence point theorems, Fixed Point Theory, 9, 487-496 (2008) · Zbl 1179.47045
[12] Ćirić, Lj.; Cakić, N., On common fixed point theorems for non-self hybrid mappings in convex metric spaces, Appl. Math. Comput., 208, 1, 90-97 (2009) · Zbl 1163.47045
[13] 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., 132, 1435-1443 (2004) · Zbl 1060.47056
[14] Nieto, J. J.; Rodriguez-Lopez, R., Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22, 223-239 (2005) · Zbl 1095.47013
[15] Bhaskar, T. Gnana; Lakshmikantham, V., Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA, 65, 1379-1393 (2006) · Zbl 1106.47047
[16] Nieto, J. J.; Lopez, R. R., Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23, 12, 2205-2212 (2007) · Zbl 1140.47045
[17] Ciric, L.; Cakic, N.; Rajovic, M.; Ume, J. S., Monotone generalized nonlinear contractions in partially ordered metric spaces, Fixed Point Theory Appl., 2008 (2008), 11 pp. Article ID 131294 · Zbl 1158.54019
[18] Harjani, J.; Sadarangani, K., Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Anal., 71, 3403-3410 (2009) · Zbl 1221.54058
[19] Ćirić, L.; Lakshmikantham, V., Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces, Stoch. Anal. Appl., 27, 6, 1246-1259 (2009) · Zbl 1176.54030
[20] Lakshmikantham, V.; Ciric, L., Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. TMA, 70, 12, 4341-4349 (2009) · Zbl 1176.54032
[21] Harjani, J.; Sadarangani, K., Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72, 1188-1197 (2010) · Zbl 1220.54025
[22] Samet, B., Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal., 72, 12, 4508-4517 (2010) · Zbl 1264.54068
[23] Karapinar, Erdal, Coupled fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl., 59, 3656-3668 (2010) · Zbl 1198.65097
[24] Abbas, M.; Khan, M. Ali; Radenovic, S., Common coupled fixed point theorems in cone metric spaces for \(w\)-compatible mappings, Appl. Math. Comput., 217, 195-202 (2010) · Zbl 1197.54049
[25] Choudhury, B. S.; Kundu, A., A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal., 73, 2524-2531 (2010) · Zbl 1229.54051
[26] Ćirić, Lj. B.; Miheţ, D.; Saadati, R., Monotone generalized contractions in partially ordered probabilistic metric spaces, Topology Appl., 156, 17, 2838-2844 (2009) · Zbl 1206.54039
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.