Fixed point theorems for \(\alpha-\beta-\psi\)-contractive mappings in partially ordered sets
-
1650
Downloads
-
2607
Views
Authors
Mohammad Sadegh Asgari
- Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Ziad Badehian
- Department of Mathematics, Faculty of Science, Central Tehran Branch, Islamic Azad University, Tehran, Iran.
Abstract
In this paper, we introduce a new concept of \(\alpha-\beta-\psi\)-contractive type mappings and construct some fixed
point theorems for such mappings in metric spaces endowed with partial order. Moreover, we use fixed
point theorems to find a solution for the first-order boundary value differential equation.
Share and Cite
ISRP Style
Mohammad Sadegh Asgari, Ziad Badehian, Fixed point theorems for \(\alpha-\beta-\psi\)-contractive mappings in partially ordered sets, Journal of Nonlinear Sciences and Applications, 8 (2015), no. 5, 518--528
AMA Style
Asgari Mohammad Sadegh, Badehian Ziad, Fixed point theorems for \(\alpha-\beta-\psi\)-contractive mappings in partially ordered sets. J. Nonlinear Sci. Appl. (2015); 8(5):518--528
Chicago/Turabian Style
Asgari, Mohammad Sadegh, Badehian, Ziad. "Fixed point theorems for \(\alpha-\beta-\psi\)-contractive mappings in partially ordered sets." Journal of Nonlinear Sciences and Applications, 8, no. 5 (2015): 518--528
Keywords
- Fixed point
- \(\alpha-\beta-\psi\)-contractive mappings
- partially ordered sets
- lower and upper solutions.
MSC
References
-
[1]
R. P. Agarwal, M. A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces , Appl. Anal., 87 (2008), 109-116.
-
[2]
I. Altun, H. Simsek , Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl., 2010 (2010), 17 pages.
-
[3]
I. Beg, A. R. Butt, Fixed point for set-valued mappings satisfying an implicit relation in partially ordered metric spaces, Nonlinear Anal., 71 (2009), 3699-3704.
-
[4]
V. Berinde, F. Vetro, Common fixed points of mappings satisfying implicit contractive conditions, Fixed Point Theory Appl., 2012 (2012), 8 pages.
-
[5]
Lj. Ćirić, N. Cakić, M. Rajović, J. Ume , Monotone Generalized Nonlinear Contractions in Partially Ordered Metric Spaces, Fixed Point Theory Appl., 2008 (2008), 11 pages.
-
[6]
M. Cosentino, P. Salimi, P. Vetro, Fixed point results on metric-type spaces, Acta Math. Sci. Ser. B Engl. Ed., 34 (2014), 1237-1253.
-
[7]
J. Harjani, K. Sadarangani , Fixed point theorems for weakly contractive mappings in partially ordered sets, Non- linear Anal., 71 (2009), 3403-3410.
-
[8]
J. Harjani, K. Sadarangani, Generalized contractions in partially ordered metric spaces and applications to ordinary differential equations, Nonlinear Anal., 72 (2010), 1188-1197.
-
[9]
P. Kumam, C. Vetro, F. Vetro, Fixed points for weak \(\alpha-\psi\)-contractions in partial metric spaces, Abstr. Appl. Anal., 2013 (2013), 9 pages.
-
[10]
G. Ladde, V. Lakshmikantham, A. Vatsala , Monotone iterative techniques for nonlinear differential equations, Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics, Pitman (Advanced Publishing Program), Boston (1985)
-
[11]
H. K. Nashine, B. Samet, Fixed point results for mappings satisfying \(\alpha-\psi\)-weakly contractive condition in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 2201-2209.
-
[12]
J. J. Nieto, R. L. Pouso, R. Rodríguez-López, Fixed point theorems in ordered abstract spaces, Proc. Amer. Math. Soc., 137 (2007), 2505-2517.
-
[13]
J. J. Nieto, R. Rodríguez-López , Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223-239.
-
[14]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.), 23 (2007), 2205-2212.
-
[15]
D. O'Regan, A. Petruşel, Fixed point theorems for generalized contractions in ordered metric spaces, J. Math. Anal. Appl., 341 (2008), 1241-1252.
-
[16]
D. Paesano, P. Vetro, Common fixed Points in a partially ordered partial metric space, Int. J. Anal., 2013 (2013), 8 pages.
-
[17]
A. C. M. Ran, M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations , Proc. Amer. Math. Soc., 132 (2003), 1435-1443.
-
[18]
B. Samet, C. Vetro, P. Vetro, Fixed point theorems for \(\alpha-\psi\)-contractive type mappings, Nonlinear Anal., 75 (2012), 2154-2165.
-
[19]
D. Turkoglu, D. Binbasioglu, Some Fixed-Point Theorems for Multivalued Monotone Mappings in Ordered Uniform Space, Fixed Point Theory Appl., 2011 (2011), 12 pages.
-
[20]
E. Zeidler, Nonlinear functional analysis and its applications, Vol. I, Springer, New York (1986)