Abstract
In this paper, we give and prove some coupled coincidence point theorems for mappings F : X × X → X and g : X → X in partially ordered metric space X, where F has the mixed g-monotone property. Our results improve and generalize the results of Bhaskar and Lakshmikantham (Nonlinear Anal TMA 65:1379–1393, 2006), Luong and Thuan (Bull Math Anal Appl 2(4):16–24, 2010), Harjani et al. (Nonlinear Anal 74:1749–1760, 2011) and Choudhury et al. (Ann Univ Ferrara 57:1–16, 2011). We also give some examples to illustrate our results.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Azam A., Arshad M., Beg I.: Coincidence and common fixed points of two maps in cone metric spaces. Rendieconti del Circolo Matematico di Palermo 57, 433–441 (2008)
Agarwal R.P., El-Gebeily M.A., O’Regan D.: Generalized contractions in partially ordered metric spaces. Appl. Anal. 87, 1–8 (2008)
Altun, I., Simsek, H.: Some fixed point theorems on ordered metric spaces and application. Fixed Point Theory Appl. 2010, 17 (2010). Article ID 621469
Choudhury B.S., Metiya N., Kundu A.: Coupled coincidence point theorems in ordered metric spaces. Ann. Univ. Ferrara 57, 1–16 (2011)
Choudhury B.S., Kundu A.: A coupled coincidence point result in partially ordered metric spaces for compatible mappings. Nonlinear Anal. 73, 2524–2531 (2010)
Ciric, L.; Cakic, N.; Rajovic, M.; Ume, J.S.: Monotone generalized nonlinear contractions in partially ordered metric spaces. Fixed Point Theory Appl. 2008, 11pp (2008). Article ID 131294
Gnana Bhaskar T., Lakshmikantham V.: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65, 1379–1393 (2006)
HarjaniJ.; Sadarangani K.: Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations. Nonlinear Anal. 72, 1188–1197 (2010)
Harjani J., Lopez B., Sadarangani K.: Fixed point theorems for mixed monotone operators and applications to integral equations. Nonlinear Anal. 74, 1749–1760 (2011)
Jachymski J.: Equivalent conditions for generalized contractions on (ordered) metric spaces. Nonlinear Analy. 74, 768–774 (2011)
Karapınar E.: Couple fixed point on cone metric spaces. Gazi Univ. J. Sci. 24(1), 51–58 (2011)
Karapınar E.: Coupled fixed point theorems for nonlinear contractions in cone metric spaces. Comput. Math. Appl. 59(12), 3656–3668 (2010)
Lakshmikantham V., Ciric L.: Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70, 4341–4349 (2009)
LuongN.V.; Thuan N.X.: Coupled fixed points in partially ordered metric spaces and application. Nonlinear Anal. 74, 983–992 (2011)
Luong N.V., Thuan N.X.: Coupled fixed point theorems in partially ordered metric spaces. Bull. Math. Anal. Appl. 2(4), 16–24 (2010)
Luong N.V., Thuan N.X.: Coupled fixed point theorems for mixed monotone mappings and an application to integral equations. Comput. Math. Appl. 62(11), 4238–4248 (2011)
Luong N.V., Thuan N.X.: Fixed point results for mappings satisfying \({(\psi,\varphi)}\) -weakly contractive condition in partially ordered metric spaces. Nonlinear Anal. 74, 2201–2209 (2011)
Nieto J.J., Rodriguez-Lopez R.: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equation. Order 22, 223–239 (2005)
Nieto J.J., Rodriguez-Lopez R.: Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Math. Sinica Engl. Ser. 23(12), 2205–2212 (2007)
O’Regan D., Petrusel A.: Fixed point theorems for generalized contractions in ordered metric spaces. J. Math. Anal. Appl. 341, 1241–1252 (2008)
Ran A.C.M., Reurings M.C.B.: A fixed point theorem in partially ordered sets and some applications to matrix equations. Proc. Am. Math. Soc. 132, 1435–1443 (2004)
Samet B.: Coupled fixed point theorems for a generalized Meir-Keeler contraction in partially ordered metric spaces. Nonlinear Anal. 72, 4508–4517 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
About this article
Cite this article
Karapınar, E., Van Luong, N. & Thuan, N.X. Coupled coincidence points for mixed monotone operators in partially ordered metric spaces. Arab. J. Math. 1, 329–339 (2012). https://doi.org/10.1007/s40065-012-0027-0
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40065-012-0027-0