×

Coupled coincidence point results for \((\psi, \alpha, \beta)\)-weak contractions in partially ordered metric spaces. (English) Zbl 1251.54056

Summary: Coupled coincidence points of mappings satisfying a nonlinear contractive condition in the framework of partially ordered metric spaces are obtained. Our results extend the results of J. Harjani, B. López and K. Sadarangani [Nonlinear Anal., Theory Methods Appl. Ser. A, Theory Methods 74, No. 5, 1749-1760 (2011; Zbl 1218.54040)]. Moreover, an example of the main result is given. Finally, some coupled coincidence point results for mappings satisfying some contraction conditions of integral type in partially ordered complete metric spaces are deduced.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems

Citations:

Zbl 1218.54040
PDF BibTeX XML Cite
Full Text: DOI

References:

[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
[2] 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
[3] L. Ćirić, N. Cakić, M. Rajović, and J. S. Ume, “Monotone generalized nonlinear contractions in partially ordered metric spaces,” Fixed Point Theory and Applications, vol. 2008, Article ID 131294, 11 pages, 2008. · Zbl 1158.54019
[4] L. Ćirić, B. Samet, N. Cakić, and B. Damjanović, “Coincidence and fixed point theorems for generalized (\psi ,\varphi )-weak nonlinear contraction in ordered K-metric spaces,” Computers & Mathematics with Applications, vol. 62, no. 9, pp. 3305-3316, 2011. · Zbl 1236.54038
[5] L. J. Ćirić, B. Samet, C. Vetro, and M. Abbas, “Fixed point results for weak contractive mappings in ordered K-metric spaces,” Fixed Point Theory and Applications, vol. 13, no. 1, pp. 59-72, 2012. · Zbl 1271.54077
[6] H. S. Ding, Z. Kadelburg, E. Karapinar, and S. Radenović, “Common fixed points of weak contractions in cone metric spaces,” Abstract and Applied Analysis, vol. 2012, Article ID 793862, 18 pages, 2012. · Zbl 1263.54050
[7] J. Harjani, B. López, and K. Sadarangani, “Fixed point theorems for mixed monotone operators and applications to integral equations,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 5, pp. 1749-1760, 2011. · Zbl 1218.54040
[8] S. Radenović, Z. Kadelburg, D. Jandrlić, and A. Jandrlić, “Some results on weakly contractive maps,” Bulletin of the Iranian Mathematical Society. In press. · Zbl 1391.54036
[9] T. Gnana Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications,” Nonlinear Analysis: Theory, Methods & Applications, vol. 65, no. 7, pp. 1379-1393, 2006. · Zbl 1106.47047
[10] V. Lakshmikantham and L. Ćirić, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 70, no. 12, pp. 4341-4349, 2009. · Zbl 1176.54030
[11] M. Abbas, M. Ali Khan, and S. Radenović, “Common coupled fixed point theorems in cone metric spaces for w-compatible mappings,” Applied Mathematics and Computation, vol. 217, no. 1, pp. 195-202, 2010. · Zbl 1197.54049
[12] H. Aydi, M. Postolache, and W. Shatanawi, “Coupled fixed point results for (\psi ,\varphi )-weakly contractive mappings in ordered G-metric spaces,” Computers & Mathematics with Applications, vol. 63, no. 1, pp. 298-309, 2012. · Zbl 1238.54020
[13] H.-S. Ding, L. Li, and S. Radenović, “Coupled coincidence point theorems for generalized nonlinear contraction in partially ordered metric spaces,” Fixed Point Theory and Applications, vol. 2012, article 96, 2012. · Zbl 1420.54071
[14] N. V. Luong and N. X. Thuan, “Coupled fixed points in partially ordered metric spaces and application,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 3, pp. 983-992, 2011. · Zbl 1202.54036
[15] W. Shatanawi, B. Samet, and M. Abbas, “Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces,” Mathematical and Computer Modelling, vol. 55, no. 3-4, pp. 680-687, 2012. · Zbl 1255.54027
[16] B. S. Choudhury and A. Kundu, “(\psi ,\alpha ,\beta )-weak contractions in partially ordered metric spaces,” Applied Mathematics Letters, vol. 25, no. 1, pp. 6-10, 2012. · Zbl 1269.54021
[17] M. S. Khan, M. Swaleh, and S. Sessa, “Fixed point theorems by altering distances between the points,” Bulletin of the Australian Mathematical Society, vol. 30, no. 1, pp. 1-9, 1984. · Zbl 0553.54023
[18] A. Branciari, “A fixed point theorem for mappings satisfying a general contractive condition of integral type,” International Journal of Mathematics and Mathematical Sciences, vol. 29, no. 9, pp. 531-536, 2002. · Zbl 0993.54040
[19] I. Altun, D. Türko\uglu, and B. E. Rhoades, “Fixed points of weakly compatible maps satisfying a general contractive condition of integral type,” Fixed Point Theory and Applications, vol. 2007, Article ID 17301, 9 pages, 2007. · Zbl 1153.54022
[20] H. K. Nashine and B. Samet, “Fixed point results for mappings satisfying (\psi ,\varphi )-weakly contractive condition in partially ordered metric spaces,” Nonlinear Analysis: Theory, Methods & Applications, vol. 74, no. 6, pp. 2201-2209, 2011. · Zbl 1208.41014
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.