Some fixed point theorems for contractive mapping in ordered vector metric spaces
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Authors
Cüneyt Çevik
- Department of Mathematics, Faculty of Science, Gazi University, 06500 Teknikokullar, Ankara, Turkey.
Ishak Altun
- Department of Mathematics, College of Science, King Saud University, Riyadh, Saudi Arabia.
- Department of Mathematics, Faculty of Science, Kırıkkale University, Kırıkkale, Turkey.
Hakan Şahin
- Department of Mathematics, Faculty of Science, Gazi University, 06500 Teknikokullar, Ankara, Turkey.
- Department of Mathematics, Faculty of Science, Amasya University, Amasya, Turkey.
Çetin Cemal Özeken
- Department of Mathematics, Faculty of Science, Gazi University, 06500 Teknikokullar, Ankara, Turkey.
Abstract
In this paper, considering an order relation on a vector metric space which is introduced by Çevik and Altun in 2009, we
present some fundamental fixed point results. Then, we provide some nontrivial examples show that the investigation of this
work is significant.
Share and Cite
ISRP Style
Cüneyt Çevik, Ishak Altun, Hakan Şahin, Çetin Cemal Özeken, Some fixed point theorems for contractive mapping in ordered vector metric spaces, Journal of Nonlinear Sciences and Applications, 10 (2017), no. 4, 1424--1432
AMA Style
Çevik Cüneyt, Altun Ishak, Şahin Hakan, Özeken Çetin Cemal, Some fixed point theorems for contractive mapping in ordered vector metric spaces. J. Nonlinear Sci. Appl. (2017); 10(4):1424--1432
Chicago/Turabian Style
Çevik, Cüneyt, Altun, Ishak, Şahin, Hakan, Özeken, Çetin Cemal. "Some fixed point theorems for contractive mapping in ordered vector metric spaces." Journal of Nonlinear Sciences and Applications, 10, no. 4 (2017): 1424--1432
Keywords
- Fixed point
- Riesz space
- vector metric space.
MSC
References
-
[1]
C. D. Aliprantis, K. C. Border, Infinite dimensional analysis: A hitchhiker’s guide, Springer-Verlag, Berlin (1999)
-
[2]
C. Çevik, On continuity of functions between vector metric spaces, J. Funct. Space, 2014 (2014 ), 6 pages.
-
[3]
C. Çevik, I. Altun, Vector metric spaces and some properties, Topol. Methods Nonlinear Anal., 34 (2009), 375–382.
-
[4]
N. Hussain, C. Vetro, F. Vetro, Fixed point results for \(\alpha\)-implicit contractions with application to integral equations, Nonlinear Anal. Model. Control, 21 (2016), 362–378.
-
[5]
P. Kumam, C. Vetro, F. Vetro, Fixed points for weak \(\alpha-\psi\)-contractions in partial metric spaces, Abstr. Appl. Anal., 2013 (2013 ), 9 pages.
-
[6]
W. A. J. Luxemburg, A. C. Zaanen, Riesz space: Vol. I, North-Holland Publishing Co., Amsterdam-London (1971)
-
[7]
J. J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order, 22 (2005), 223–239.
-
[8]
J. J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations, Acta Mathematica Sinica (English Series), 23 (2007), 2205–2212.
-
[9]
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 (2004), 1435–1443.