In this paper we obtain existence and uniqueness results for quadruple fixed points of operators $F: X^4 \rightarrow X$. We also give some examples to support our results.
References
R.P. Agarwal, M.A. El-Gebeily and D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), no. 1, 1–8. MR2381749 10.1080/00036810701556151 R.P. Agarwal, M.A. El-Gebeily and D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), no. 1, 1–8. MR2381749 10.1080/00036810701556151
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. 72 (2010) 2238–2242. MR2577790 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. 72 (2010) 2238–2242. MR2577790
I. Altun, B. Damjanovic and D. Djoric, Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett. 23 (2010), 310–316. MR2565197 10.1016/j.aml.2009.09.016 I. Altun, B. Damjanovic and D. Djoric, Fixed point and common fixed point theorems on ordered cone metric spaces, Appl. Math. Lett. 23 (2010), 310–316. MR2565197 10.1016/j.aml.2009.09.016
V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), 4889–4897. MR2810674 V. Berinde and M. Borcut, Tripled fixed point theorems for contractive type mappings in partially ordered metric spaces, Nonlinear Anal. 74 (2011), 4889–4897. MR2810674
T.G. Bhaskar and V. Lakshmikantham, Fixed Point Theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379–1393. MR2245511 T.G. Bhaskar and V. Lakshmikantham, Fixed Point Theory in partially ordered metric spaces and applications, Nonlinear Anal. 65 (2006), 1379–1393. MR2245511
Binayak S. Choudhury, N. Metiya and A. Kundu, Coupled coincidence point theorems in ordered metric spaces, Ann. Univ. Ferrara 57 (2011), 1–16. MR2821367 05947320 10.1007/s11565-011-0117-5 Binayak S. Choudhury, N. Metiya and A. Kundu, Coupled coincidence point theorems in ordered metric spaces, Ann. Univ. Ferrara 57 (2011), 1–16. MR2821367 05947320 10.1007/s11565-011-0117-5
B.S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal. 73 (2010), no. 8, 2524–2531. MR2674088 B.S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal. 73 (2010), no. 8, 2524–2531. MR2674088
R.H. Haghi, Sh. Rezapour and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal. 74 (2011), no. 5, 1799–1803. MR2764380 R.H. Haghi, Sh. Rezapour and N. Shahzad, Some fixed point generalizations are not real generalizations, Nonlinear Anal. 74 (2011), no. 5, 1799–1803. MR2764380
E. Karap\i nar, Coupled fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl. 59 (2010), no. 12, 3656–3668. MR2651841 E. Karap\i nar, Coupled fixed point theorems for nonlinear contractions in cone metric spaces, Comput. Math. Appl. 59 (2010), no. 12, 3656–3668. MR2651841
V. Lakshmikantham and L. Ćirić, Couple Fixed Point Theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341–4349. MR2514765V. Lakshmikantham and L. Ćirić, Couple Fixed Point Theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal. 70 (2009), 4341–4349. MR2514765
B. Monjardet, Metrics on partially ordered sets- A survey, Discrete Math. 35 (1981), 173–184. MR620670 0463.46016 10.1016/0012-365X(81)90206-5 B. Monjardet, Metrics on partially ordered sets- A survey, Discrete Math. 35 (1981), 173–184. MR620670 0463.46016 10.1016/0012-365X(81)90206-5
A.C.M. Ran and M.C.B. Reurings,A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435–1443. MR2053350 1060.47056 10.1090/S0002-9939-03-07220-4 A.C.M. Ran and M.C.B. Reurings,A fixed point theorem in partially ordered sets and some application to matrix equations, Proc. Amer. Math. Soc., 132 (2004), 1435–1443. MR2053350 1060.47056 10.1090/S0002-9939-03-07220-4
E.S. Wolk, Continuous convergence in partially ordered sets, General Topology Appl. 5 (1975), no. 3, 221–234. MR380704 10.1016/0016-660X(75)90022-7 E.S. Wolk, Continuous convergence in partially ordered sets, General Topology Appl. 5 (1975), no. 3, 221–234. MR380704 10.1016/0016-660X(75)90022-7
