Document Type : Research Paper
Author
- Hasan Hosseinzadeh ^{} ^{}
Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.
Abstract
Let $\mathcal{X}$ be a partially ordered set and $d$ be a generalized metric on $\mathcal{X}$. We obtain some results in coupled and coupled coincidence of $g$-monotone functions on $\mathcal{X}$, where $g$ is a function from $\mathcal{X}$ into itself. Moreover, we show that a nonexpansive mapping on a partially ordered Hilbert space has a fixed point lying in the unit ball of the Hilbert space. Some applications for linear and nonlinear matrix equations are given.
Keywords
[1] G. Allaire and S. M. Kaber, Numerical linear algebra, Vol. 55 of Texts in Applied Mathematics, Springer-New York, 2008.
[2] T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65(2006),pp. 1379-1393.
[3] A. D. Filip and Petrusel, Fixed point theorems on spaces endowed with vector-valued metrics, Fixed Point Theory and Applications, 20 (2010).
[4] H. Hosseinzadeh, A. Jabbari and A. Razani, Fixed point and common fixed point theorems on spaces which endowed vector-valued metrics, Ukrainian J. Math., 65 (50)(2013), pp. 814-822.
[5] R. Precup, The role of matrices that are convergent to zero in the study of semilinear operator systems, Mathematical and Computer Modelling, 49(3-4) (2009), pp. 703-708.
[6] A. C. M. Ran and M. C. B. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc., 132(5) (2003), pp. 1435-1443.
[7] A. Razani, H. Hosseinzadeh and A. Jabbari, Coupled fixed point theorems in partially ordered metric spaces which endowed vector-valued metrics, Aust. J. Basic and App. Sci., 6(2)(2012),pp. 124-129.
[8] B. Ricceri, Another fixed point theorem for nonexpansive potential operators, Studia Math., 211(2)(2012), pp. 147-151.
[9] I. A. Rus, Principles and applications of the fixed point theory, Dacia, Cluj-Napoca, Romania, 1979.
[10] R. S. Varga, Matrix iterative analysis, Vol. 27 of Springer Series in Computational Mathematics, Springer-Berlin, 2000.