Tripled and coincidence fixed point theorems for contractive mappings satisfying Φ-maps in partially ordered metric spaces

Shatanawi, Wasfi; Postolache, Mihai; Mustafa, Zead

doi:10.2478/auom-2014-0058

Abstract

In this paper, we study some tripled fixed and coincidence point theorems for two mappings F : X × X × X → X and ɡ : X → X satisfying a nonlinear contraction based on ϕ-maps. Our results extend and improve many existing results in the literature. Also, we introduce an example to support the validity of our results.

References

[1] T. G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379–1393.10.1016/j.na.2005.10.017
Search in Google Scholar
[2] V. Lakshmikantham, Lj. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341–4349.10.1016/j.na.2008.09.020
Search in Google Scholar
[3] V. Berinde, M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), 4889–4897.10.1016/j.na.2011.03.032
Search in Google Scholar
[4] M. Borcut, V. Berinde, Tripled coincidence theorems for contractive type mappings in partially ordered metric spaces, Appl. Math. Comput. 218 (2012), 5929-5936.
Search in Google Scholar
[5] H. Aydi, M. Postolache, W. Shatanawi, Coupled fixed point results for (psi, phi)-weakly contractive mappings in ordered G-metric spaces, Comput. Math. Appl. 63 (2012), 298–309.10.1016/j.camwa.2011.11.022
Search in Google Scholar
[6] H. Aydi, E. Karapinar, M. Postolache, Tripled coincidence point theorems for weak phi-contractions in partially ordered metric spaces, Fixed Point Theory Appl., Vol. 2012, ID: 2012:44, 12 pp.10.1186/1687-1812-2012-44
Search in Google Scholar
[7] V. Berinde, Coupled coincidence point theorems for mixed monotone nonlinear operators, Comput. Math. Appl. 64 (2012), 1770–1777.10.1016/j.camwa.2012.02.012
Search in Google Scholar
[8] V. Berinde, Coupled fixed point theorems for ϕ-contractive mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal. 75 (2012), 3218-3228.10.1016/j.na.2011.12.021
Search in Google Scholar
[9] S. Chandok, Z. Mustafa, M. Postolache, Coupled common fixed point theorems for mixed g-monotone mappings in partially ordered G-metric spaces, U. Politeh. Buch. Ser. A, 75 (2013), No. 4, 13-26.
Search in Google Scholar
[10] D. Dorić, Z. Kadelburg, S. Radenović, Coupled fixed point results for mappings without mixed monotone property, Appl. Math. Lett. 25 (2012), 1803-1808.10.1016/j.aml.2012.02.022
Search in Google Scholar
[11] B. S. Choudhury, N. Metiya, M. Postolache, A generalized weak contraction principle with applications to coupled coincidence point problems, Fixed Point Theory Appl., Vol. 2013, ID: 2013:152, 21 pp.10.1186/1687-1812-2013-152
Search in Google Scholar
[12] N. V. Luong, N. X. Thuan, Coupled fixed points in partially ordered metric spaces and applications, Nonlinear Anal. 72 (2011), 983–992.10.1016/j.na.2010.09.055
Search in Google Scholar
[13] Z. Golubović, Z. Kadelburg, S. Radenović, Coupled coincidence points of mappings in ordered partial metric spaces, Abstr. Appl. Anal. 2012 (2012), art. no. 192581.
Search in Google Scholar
[14] H. K. Nashine and W. Shatanawi, Coupled common fixed point theorems for a pair of commuting mappings in partially ordered complete metric spaces, Comput. Math. Appl. 62 (2011), 1984–1993.10.1016/j.camwa.2011.06.042
Search in Google Scholar
[15] H. K. Nashine, Z. Kadelburg, S. Radenović, Coupled common fixed point theorems for w-compatible mappings in ordered cone metric spaces, Appl. Math. Comput. 218 (2012), 5422-5432.
Search in Google Scholar
[16] B. Samet, Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces, Nonlinear Anal. 72 (2010), 4508–4517.10.1016/j.na.2010.02.026
Search in Google Scholar
[17] B. Samet, C. Vetro, Coupled fixed point, F-invariant set and fixed point of N-order, Ann. Funct. Anal. 1 (2) (2010), 46–56.10.15352/afa/1399900586
Search in Google Scholar
[18] B. Samet, C. Vetro, Coupled fixed point theorems for multi-valued nonlinear contraction mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), 4260–426810.1016/j.na.2011.04.007
Search in Google Scholar
[19] B. Samet, H. Yazidi, Coupled fixed point theorems in partially ordered ε-chainable metric spaces, TJMCS. 1 (3) (2010), 142–151.10.22436/jmcs.001.03.02
Search in Google Scholar
[20] W. Shatanawi, A. Pitea, Fixed and coupled fixed point theorems of omega-distance for nonlinear contraction. Fixed Point Theory Appl., Vol. 2013, ID: 2013:275, 16 pp.10.1186/1687-1812-2013-275
Search in Google Scholar
[21] W. Shatanawi, A. Pitea, Omega-distance and coupled fixed point in G-metric spaces. Fixed Point Theory Appl., Vol. 2013, Article ID: 2013:208, 15 pp.10.1186/1687-1812-2013-208
Search in Google Scholar
[22] W. Shatanawi, A. Pitea, Some coupled fixed point theorems in quasi-partial metric spaces. Fixed Point Theory Appl., Vol. 2013, ID: 2013:153, 13 pp.10.1186/1687-1812-2013-153
Search in Google Scholar
[23] W. Shatanawi, Z. Mustafa, On coupled random fixed point results in partially ordered metric spaces, Matematicki Vesnik, 64 (2012), 139–146.
Search in Google Scholar
[24] W. Shatanawi, Coupled fixed point theorems in generalized metric spaces, Hacettepe J. Mathematics and Statistics, Volume 40 (3) (2011), 441–447.10.1186/1687-1812-2011-80
Search in Google Scholar
[25] W. Shatanawi, Fixed point theorems for nonlinear weakly C-contractive mappings in metric spaces, Math. Comput. Modelling 54 (2011), 2816–2826, doi:10.1016/j.mcm.2011.06.06910.1016/j.mcm.2011.06.069
Search in Google Scholar
[26] J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proceedings of the American Mathematical Society, 62 (2) (1977), pp. 344–348.
Search in Google Scholar

Tripled and coincidence fixed point theorems for contractive mappings satisfying Φ-maps in partially ordered metric spaces

Abstract

Paradigm

My account