# Journal of Advances in Applied Mathematics

### Partial Coupled Fixed Points and Coupled Fixed Points

Download PDF (524.2 KB) PP. 183 - 194 Pub. Date: July 12, 2016

### Author(s)

**Marta Demma**

Dipartimento di Matematica e Informatica, University of Palermo, Via Archirafi n. 34, 90123 Palermo, Italy**Peyman Salimi**

Department of Mathematics, Sahand University of Technology, Tabriz, Iran**Pasquale Vetro**^{*}

Dipartimento di Matematica e Informatica, University of Palermo, Via Archirafi n. 34, 90123 Palermo, Italy

### Abstract

### Keywords

### References

[1] R. P. Agarwal, M. A. El-Gebeily and D. O’Regan, “Generalized contractions in partially ordered metric spaces”, Appl. Anal., vol. 87, 1–8, 2008.

[2] I. Altun and H. Simsek, “Some fixed point theorems on ordered metric spaces and application”, Fixed Point Theory Appl., vol. 2010, Article ID 621492, pp. 1–20, 2010.

[3] A. Amini-Harandi and H. Emami, “A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary differential equations”, Nonlinear Anal., vol. 72, pp. 2238–2242, 2010.

[4] T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications”, Nonlinear Anal., vol. 65, pp. 1379–1393, 2006.

[5] B. Choudhury and A. Kundu, “A coupled coincidence point result in partially ordered metric spaces for compatible mappings”, Nonlinear Anal., vol. 73, pp. 2524–2531, 2010.

[6] Lj. B. Ciric, N. Cakic, M. Rajovic and J. S. Ume, “Monotone generalized nonlinear contractions in partially ordered metric spaces”, Fixed point Theory Appl., vol. 2008, Article ID 131294, pp. 1–11, 2008.

[7] Lj. B. Ciric, B. Samet, H. Aydi and C. Vetro, “Common fixed points of generalized contractions on partial metric spaces and an application”, Appl. Math. Comput., vol. 218, pp. 2398–2406, 2011.

[8] J. Harjani and K. Sadarangani, “Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations”, Nonlinear Anal., vol. 72, pp. 1188–1197, 2010.

[9] N. Hussain, M. H. Shah and M. A. Kutbi, “Coupled coincidence point theorems for nonlinear contractions in partially ordered quasi-metric spaces with a Q-function”, Fixed point Theory Appl., vol. 2011, Article ID 703938, pp. 1–21, 2011.

[10] V. Lakshmikantham and Lj. B. Ciric, “Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces”, Nonlinear Anal., vol. 70, pp. 4341–4349, 2009.

[11] S. G. Matthews, “Partial metric topology”, in Proc. 8th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., vol. 728, 1994, pp. 183–197.

[12] H. K. Nashine and I. Altun, “Fixed point theorems for generalized weakly contractive condition in ordered metric spaces”, Fixed point Theory Appl., vol. 2011, Article ID 132367, pp. 1–20, 2011.

[13] H. K. Nashine and B. Samet, “Fixed point results for mappings satisfying ( , )-weakly contractive condition in partially ordered metric spaces”, Nonlinear Anal., vol. 74, pp. 2201–2209, 2011.

[14] H. K. Nashine, B. Samet and C. Vetro, “Monotone generalized nonlinear contractions and fixed point theorems in ordered metric spaces”, Math. Comput. Modelling, vol. 54, pp. 712–720, 2011.

[15] S. J. O’Neill, “Partial metrics, valuations and domain theory”, in Proc. 11th Summer Conference on General Topology and Applications, Ann. New York Acad. Sci., vol. 806, 1996, pp. 304–315.

[16] J. J. Nieto and R. Rodríguez-López, “Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations”, Order, vol. 22, pp. 223–239, 2005.

[17] J. J. Nieto and R. Rodríguez-López, “Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations”, Acta Math. Sinica (Engl. Ser.), vol. 23, pp 2205–2212, 2007.

[18] S. Oltra and O. Valero, “Banach’s fixed point theorem for partial metric spaces”, Rend. Istit. Mat. Univ. Trieste, vol. 36, pp. 17–26, 2004.

[19] D. Paesano and P. Vetro, “Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces”, Topology Appl., vol. 159, pp. 911–920, 2012.

[20] A. C. M. Ran and M. C. B. Reurings, “A fixed point theorem in partially ordered sets and some applications to matrix equations”, Proc. Amer. Math. Soc., vol. 132, pp. 1435–1443, 2004.

[21] D. O’Regan and A. Petrutel, “Fixed point theorems for generalized contractions in ordered metric spaces”, J. Math. Anal. Appl., vol. 341, pp. 1241–1252, 2008.

[22] S. Romaguera, “A Kirk type characterization of completeness for partial metric spaces”, Fixed Point Theory Appl., vol. 2010, Article ID 493298, pp. 1–6, 2010.

[23] B. Samet, “Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces”, Nonlinear Anal., vol. 72, pp. 4508–4517, 2010.

[24] W. Shatanawi, “Partially ordered cone metric spaces and coupled fixed point results”, Comput. Math. Appl., vol. 60, pp. 2508–2515, 2010.

[25] O. Valero, “On Banach fixed point theorems for partial metric spaces”, Appl. Gen. Topol., vol. 6, pp. 229–240, 2005.

[26] Y. Wu, “New fixed point theorems and applications of mixed monotone operator”, J. Math. Anal. Appl., vol. 341, pp. 883–893, 2008.

[27] Y.Wu and Z. Liang, “Existence and uniqueness of fixed points for mixed monotone operators with applications”, Nonlinear Anal., vol. 65, pp. 1913–1924, 2006.