Tripled coincidence and fixed point results in partial metric spaces

Hassen Aydi, Mujahid Abbas

Abstract

In this paper, we introduce the concept of W-compatiblity of mappings F : X × X × X ! X and g : X ! X and based on this notion, we obtain tripled coincidence and common tripled fixed point results in the setting of partial metric spaces. The presented results generalize and extend several well known comparable results in the existing literature. We also provide an example to support our results.

Keywords

W-compatible mappings; Tripled coincidence point; Common tripled fixed point; Partial metric space

Subject classification

54H25; 47H10

Full Text:

PDF

References

M. Abbas, M. Ali Khan and S. Radenovic, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput. 217 (2010), 195-202. https://doi.org/10.1016/j.amc.2010.05.042

T. Abedelljawad, E. Karapınar and K. Tas, Existence and uniqueness of common fixed point on partial metric spaces, Appl. Math. Lett. 24 (2011), 1894-1899. https://doi.org/10.1016/j.aml.2011.05.013

I. Altun, F. Sola and H. Simsek, Generalized contractions on partial metric spaces, Topology and its Appl. 157 (2010), 2778-2785. https://doi.org/10.1016/j.topol.2010.08.017

I. Altun and A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl. 2011 (2011), Article ID 508730, 10 pages. https://doi.org/10.1155/2011/508730

H. Aydi, Some coupled fixed point results on partial metric spaces, International J. Math. Math. Sciences 2011 (2011), Article ID 647091, 11 pages. https://doi.org/10.1155/2011/647091

H. Aydi, Some fixed point results in ordered partial metric spaces, The J. Nonlinear Sci. Appl. 4, no. 2 (2011), 210-217. https://doi.org/10.22436/jnsa.004.03.04

H. Aydi, Fixed point results for weakly contractive mappings in ordered partial metric spaces, Journal of Advanced Mathematical Studies 4, no. 2 (2011), 1-12. https://doi.org/10.3366/nor.2011.0002

H. Aydi, Fixed point theorems for generalized weakly contractive condition in ordered partial metric spaces, Journal of Nonlinear Analysis and Optimization: Theory and Applications 2, no. 2 (2011), 33-48.

H. Aydi, Common fixed point results for mappings satisfying (v,o)-weak contractions in ordered partial metric spaces, International J. Mathematics and Statistics 12, no. 2 (2012), 53-64.

H. Aydi, E. Karapınar and W. Shatanawi, Coupled fixed point results for (v,y)-weakly contractive condition in ordered partial metric spaces, Comput. Math. Appl. 62 (2011), 4449-4460. https://doi.org/10.1016/j.camwa.2011.10.021

H. Aydi, B. Samet and C. Vetro, Coupled fixed point results in cone metric spaces for w-compatible mappings, Fixed Point Theory Appl. 2011, 2011:27. https://doi.org/10.1186/1687-1812-2011-27

V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74, no. 15 (2011), 4889-4897. https://doi.org/10.1016/j.na.2011.03.032

T. G. Bhashkar and V. Lakshmikantham, Fixed point theorems in partially ordered cone metric spaces and applications, Nonlinear Anal. 65 (2006), 825-832. https://doi.org/10.1016/j.na.2005.10.015

L.j. Ciric, B. Samet, H. Aydi and C. Vetro, Common fixed points of generalized contractions on partial metric spaces and an application, Appl. Math. Comput. 218 (2011), 2398-2406. https://doi.org/10.1016/j.amc.2011.07.005

E. Karapınar and I. M. Erhan, Fixed point theorems for operators on partial metric spaces, Appl. Math. Lett. 24 (2011), 1900-1904. https://doi.org/10.1016/j.aml.2011.05.013

E. Karapınar, Generalizations of Caristi Kirk's theorem on partial metric spaces, Fixed Point Theory Appl. (2011), 2011:4. https://doi.org/10.1186/1687-1812-2011-4

E. Karapınar and U. Yuksel, Some common fixed point theorems in partial metric spaces, Journal of Applied Mathematics 2011 (2011), Article ID 263621, 17 pages. https://doi.org/10.1186/1687-1812-2011-4

V. Lakshmikantham and L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341-4349. https://doi.org/10.1016/j.na.2008.09.020

S. G. Matthews, Partial metric topology. Research Report 212. Dept. of Computer Science. University of Warwick, 1992.

S. G. Matthews, Partial metric topology. In General Topology and its Applications. Proc. 8th Summer Conf., Queen's College (1992). Annals of the New York Academy of Sciences, vol. 728 (1994), 183-197. https://doi.org/10.1111/j.1749-6632.1994.tb44144.x

B. Samet and C. Vetro, Coupled fixed point, f-invariant set and fixed point of N-order, Ann. Funct. Anal. 1, no. 2 (2010), 46-56. https://doi.org/10.15352/afa/1399900586

W. Shatanawi, B. Samet and M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling 55 (2012), 680-687. https://doi.org/10.1016/j.mcm.2011.08.042

S. Oltra and O. Valero, Banach's fixed point theorem for partial metric spaces, Rendiconti dell'Istituto di Matematica dell'Universit di Trieste 36, no. 1-2 (2004), 17-26.

O. Valero, On Banach fixed point theorems for partial metric spaces, Applied General Topology 6, no. 2 (2005), 229-240. https://doi.org/10.4995/agt.2005.1957

Abstract Views

1528
Metrics Loading ...

Metrics powered by PLOS ALM




Esta revista se publica bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.

Universitat Politècnica de València

e-ISSN: 1989-4147   https://doi.org/10.4995/agt