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Some fixed point theorems in ordered $G$-metric spaces and applications. (English) Zbl 1217.54057
Summary: We study a number of fixed point results for the two weakly increasing mappings $f$ and $g$ with respect to partial ordering relation $\preceq$ in generalized metric spaces. An application to integral equations is given.

54H25Fixed-point and coincidence theorems in topological spaces
Full Text: DOI
[1] A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations,” Proceedings of the American Mathematical Society, vol. 132, no. 5, pp. 1435-1443, 2004. · Zbl 1060.47056 · doi:10.1090/S0002-9939-03-07220-4
[2] R. P. Agarwal, M. A. El-Gebeily, and D. O’Regan, “Generalized contractions in partially ordered metric spaces,” Applicable Analysis, vol. 87, no. 1, pp. 109-116, 2008. · Zbl 1140.47042 · doi:10.1080/00036810701556151
[3] J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations,” Order, vol. 22, no. 3, pp. 223-239, 2005. · Zbl 1095.47013 · doi:10.1007/s11083-005-9018-5
[4] J. J. Nieto and R. Rodríguez-López, “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations,” Acta Mathematica Sinica, vol. 23, no. 12, pp. 2205-2212, 2007. · Zbl 1140.47045 · doi:10.1007/s10114-005-0769-0
[5] J. J. Nieto, R. L. Pouso, and R. Rodríguez-López, “Fixed point theorems in ordered abstract spaces,” Proceedings of the American Mathematical Society, vol. 135, no. 8, pp. 2505-2517, 2007. · Zbl 1126.47045 · doi:10.1090/S0002-9939-07-08729-1
[6] D. O’Regan and A. Petru\csel, “Fixed point theorems for generalized contractions in ordered metric spaces,” Journal of Mathematical Analysis and Applications, vol. 341, no. 2, pp. 2505-2517, 2007. · doi:10.1016/j.jmaa.2007.11.026
[7] Z. Mustafa and B. Sims, “A new approach to generalized metric spaces,” Journal of Nonlinear and Convex Analysis, vol. 7, no. 2, pp. 289-297, 2006. · Zbl 1111.54025
[8] Z. Mustafa and B. Sims, “Some remarks concerning D-metric spaces,” in Proceedings of the International Conference on Fixed Point Theory and Applications, pp. 189-198, Valencia, Spain, July 2003. · Zbl 1079.54017
[9] Z. Mustafa, W. Shatanawi, and M. Bataineh, “Existence of fixed point results in G-metric spaces,” International Journal of Mathematics and Mathematical Sciences, vol. 2009, Article ID 283028, 10 pages, 2009. · Zbl 1179.54066 · doi:10.1155/2009/283028 · eudml:45716
[10] Z. Mustafa, H. Obiedat, and F. Awawdeh, “Some fixed point theorem for mapping on complete G-metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 189870, 12 pages, 2008. · Zbl 1148.54336 · doi:10.1155/2008/189870 · eudml:54664
[11] M. Abbas and B. E. Rhoades, “Common fixed point results for noncommuting mappings without continuity in generalized metric spaces,” Applied Mathematics and Computation, vol. 215, no. 1, pp. 262-269, 2009. · Zbl 1185.54037 · doi:10.1016/j.amc.2009.04.085
[12] R. Chugh, T. Kadian, A. Rani, and B. E. Rhoades, “Property p in G-metric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 401684, 12 pages, 2010. · Zbl 1203.54037 · doi:10.1155/2010/401684 · eudml:227131
[13] R. Saadati, S. M. Vaezpour, P. Vetro, and B. E. Rhoades, “Fixed point theorems in generalized partially ordered G-metric spaces,” Mathematical and Computer Modelling, vol. 52, no. 5-6, pp. 797-801, 2010. · Zbl 1202.54042 · doi:10.1016/j.mcm.2010.05.009
[14] W. Shatanawi, “Fixed point theory for contractive mappings satisfying \Phi -maps in Gmetric spaces,” Fixed Point Theory and Applications, vol. 2010, Article ID 181650, 9 pages, 2010. · Zbl 1204.54039 · doi:10.1155/2010/181650 · eudml:232392
[15] H. Aydi, B. Damjanović, B. Samet, and W. Shatanawi, “Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces,” Mathematical and Computer Modelling. In press. · Zbl 1237.54043 · doi:10.1016/j.mcm.2011.05.059
[16] I. Altun and H. Simsek, “Some fixed point theorems on ordered metric spaces and application,” Fixed Point Theory and Applications, vol. 2010, Article ID 621469, 17 pages, 2010. · Zbl 1197.54053 · doi:10.1155/2010/621469 · eudml:226094
[17] B. Ahmed and J. J. Nieto, “The monotone iterative technique for three-point secondorder integrodifferential boundary value problems with p-Laplacian,” Boundary Value Problems, vol. 2007, Article ID 57481, 9 pages, 2007. · Zbl 1149.65098 · doi:10.1155/2007/57481 · eudml:54721
[18] A. Cabada and J. J. Nieto, “Fixed points and approximate solutions for nonlinear operator equations,” Journal of Computational and Applied Mathematics, vol. 113, no. 1-2, pp. 17-25, 2000. · Zbl 0954.47038 · doi:10.1016/S0377-0427(99)00240-X
[19] J. J. Nieto, “An abstract monotone iterative technique,” Nonlinear Analysis: Theory Method and Applications, vol. 28, no. 12, pp. 1923-1933, 1997. · Zbl 0883.47058 · doi:10.1016/S0362-546X(97)89710-6