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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:
54H25Fixed-point and coincidence theorems in topological spaces
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
References:
[1]Z. Mustafa, B. Sims, Some remarks concerning D-metric spaces, in: Proc. Int. Conf. on Fixed Point Theor. Appl., Valencia, Spain, July 2003, pp. 189–198. · Zbl 1079.54017
[2]Mustafa, Z.; Sims, B.: A new approach to generalized metric spaces, J. nonlinear convex anal. 7, No. 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) · Zbl 1148.54336 · doi:10.1155/2008/189870
[4]Mustafa, Z.; Shatanawi, W.; Bataineh, M.: Fixed point theorems on uncomplete G-metric spaces, J. math. Stat. 4, No. 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) · Zbl 1179.54066 · doi:10.1155/2009/283028
[6]Mustafa, Z.; Sims, B.: Fixed point theorems for contractive mappings in complete G-metric space, Fixed point theory appl. 2009 (2009) · Zbl 1179.54067 · doi:10.1155/2009/917175
[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 · doi:10.1016/j.amc.2009.04.085
[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 · doi:10.1016/j.mcm.2010.05.009
[9]Chugh, Renu; Kadian, Tamanna; Rani, Anju; Rhoades, B. E.: Property P in G-metric spaces, Fixed point theory appl. 2010 (2010) · Zbl 1203.54037 · doi:10.1155/2010/401684
[10]Abbas, Mujahid; Nazir, Talat; Radenovic, Stojan: Some periodic point results in generalized metric spaces, Appl. math. Comput. 217, No. 8, 4094-4099 (2010) · Zbl 1210.54049 · doi:10.1016/j.amc.2010.10.026
[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, No. 1, 90-97 (2009) · Zbl 1163.47045 · doi:10.1016/j.amc.2008.11.012
[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 · doi:10.1090/S0002-9939-03-07220-4
[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 · doi:10.1007/s11083-005-9018-5
[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 · doi:10.1016/j.na.2005.10.017
[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, No. 12, 2205-2212 (2007) · Zbl 1140.47045 · doi:10.1007/s10114-005-0769-0
[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) · Zbl 1158.54019 · doi:10.1155/2008/131294
[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 · doi:10.1016/j.na.2009.01.240
[19]Ćirić, L.; Lakshmikantham, V.: Coupled random fixed point theorems for nonlinear contractions in partially ordered metric spaces, Stoch. anal. Appl. 27, No. 6, 1246-1259 (2009) · Zbl 1176.54030 · doi:10.1080/07362990903259967
[20]Lakshmikantham, V.; Ciric, L.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear anal. TMA 70, No. 12, 4341-4349 (2009) · Zbl 1176.54032 · doi:10.1016/j.na.2008.09.020
[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 · doi:10.1016/j.na.2009.08.003
[22]Samet, B.: Coupled fixed point theorems for a generalized Meir–Keeler contraction in partially ordered metric spaces, Nonlinear anal. 72, No. 12, 4508-4517 (2010)
[23]Karapinar, Erdal: Coupled fixed point theorems for nonlinear contractions in cone metric spaces, Comput. math. Appl. 59, 3656-3668 (2010) · Zbl 1198.65097 · doi:10.1016/j.camwa.2010.03.062
[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 · doi:10.1016/j.amc.2010.05.042
[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 · doi:10.1016/j.na.2010.06.025
[26]Ćirić, Lj.B.; Miheţ, D.; Saadati, R.: Monotone generalized contractions in partially ordered probabilistic metric spaces, Topology appl. 156, No. 17, 2838-2844 (2009) · Zbl 1206.54039 · doi:10.1016/j.topol.2009.08.029