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Coupled common fixed point results in two generalized metric spaces. (English) Zbl 1210.54048
Summary: Study of necessary conditions for the existence of a unique coupled common fixed point of contractive type mappings in the context of two generalized metric spaces is initiated. These results generalize several comparable results from the current literature. We also provide illustrative examples in support of our new results.

54H25Fixed-point and coincidence theorems in topological spaces
Full Text: DOI
[1] Abbas, M.; Rhoades, B. E.: Common fixed point results for non-commuting mappings without continuity in generalized metric spaces, Appl. math. Comput. 215, 262-269 (2009) · Zbl 1185.54037 · doi:10.1016/j.amc.2009.04.085
[2] Abbas, M.; Khan, M. A.; Radenović, S.: Common coupled fixed point theorem in cone metric space for w-compatible mappings, Appl. math. Comput. 217, 195-202 (2010) · Zbl 1197.54049 · doi:10.1016/j.amc.2010.05.042
[3] Abbas, M.; Nazir, T.; Radenović, S.: Some periodic point results in generalized metric spaces, Appl. math. Comput. 217, 195-202 (2010) · Zbl 1210.54049 · doi:10.1016/j.amc.2010.10.026
[4] Agarwal, R. P.; El-Gebeily, M. A.; O’regan, D.: Generalized contractions in partially ordered metric spaces, Appl. anal. 87, 1-8 (2008) · Zbl 1140.47042 · doi:10.1080/00036810701556151
[5] Bhashkar, T. G.; Lakshmikantham, V.: Fixed point theorems in partially ordered metric spaces and applications, Nonlinear anal. 65, 1379-1393 (2006) · Zbl 1106.47047 · doi:10.1016/j.na.2005.10.017
[6] Kadelburg, Z.; Radenović, S.; Rakočević, V.: A note on equivalence of some metric and cone metric fixed point results, Appl. math. Lett. 24, 370-374 (2011) · Zbl 1213.54067 · doi:10.1016/j.aml.2010.10.030
[7] Khan, A. R.; Domlo, A. A.; Hussain, N.: Coincidences of Lipschitz type hybrid maps and invariant approximation, Numer. funct. Anal. opt. 28, No. 9 -- 10, 1165-1177 (2007) · Zbl 1145.54040 · doi:10.1080/01630560701563859
[8] Lakshmikantham, V.; &cacute, Lj.; Irić: Coupled fixed point theorems for nonlinear contractions in partially ordered metric space, Nonlinear anal. 70, 4341-4349 (2009) · Zbl 1176.54032
[9] Z. Mustafa, B. Sims, Some remarks concerning D-metric spaces, in: Proceedings of the International Conference on Fixed Point Theory Appl., Valencia (Spain), July 2003, pp. 189 -- 198. · Zbl 1079.54017
[10] Mustafa, Z.; Sims, B.: A new approach to generalized metric spaces, J. nonlinear convex anal. 7, No. 2, 289-297 (2006) · Zbl 1111.54025
[11] Z. Mustafa, H. Obiedat, F. Awawdehand, Some fixed point theorem for mapping on complete G-metric spaces, Fixed Point Theory Appl., vol. 2008, Article ID 189870, 12 p., doi:10.1155/2008/189870. · Zbl 1148.54336 · doi:10.1155/2008/189870
[12] Z. Mustafa and B. Sims, Fixed point theorems for contractive mapping in complete G-metric spaces, Fixed Point Theory Appl., vol. 2009, Article ID 917175, 10 p., doi:0.1155/2009/917175. · Zbl 1179.54067 · doi:10.1155/2009/917175
[13] Mustafa, Z.; Awawdeh, F.; Shatanawi, W.: Fixed point theorem for expansive mappings in G-metric spaces, Int. J. Contemp. math. Sci. 5, 2463-2472 (2010) · Zbl 1284.54065
[14] Saadati, R.; Vaezpour, S. M.; Vetro, P.; Rhoades, B. E.: Fixed point theorems in generalized partially ordered G-metric spaces, Math. comput. Modell. 52, 797-801 (2010) · Zbl 1202.54042 · doi:10.1016/j.mcm.2010.05.009
[15] F. Sabetghadam, H.P. Masiha, A.H. Sanatpour, Some coupled fixed point theorems in cone metric spaces, Fixed Point Theory Appl., vol. 2009, Article ID 125426, 8 p., doi:10.1155/2009/125426. · Zbl 1179.54069 · doi:10.1155/2009/125426
[16] W. Shatanawi, Fixed point theory for contractive mappings satisfying \Phi -maps in G-metric spaces, Fixed Point Theory Appl., vol. 2010, Article ID 181650, 9 p., doi:10.1155/2010/181650. · Zbl 1204.54039 · doi:10.1155/2010/181650