Fixed points of mixed non-monotone tripled operators in ordered Banach spaces and applications
-
1635
Downloads
-
2362
Views
Authors
Xiaoyan Zhang
- School of Mathematics, Shandong University, Jinan 250100, Shandong, China.
Abstract
This paper is concerned with a class of mixed non-monotone tripled operators under the general conditions
of ordering relations in ordered Banach spaces. By means of the cone theory and technique of
equivalent norms, the existence and uniqueness of fixed points for such tripled operators are established.
The proof method in this paper is different from those used in the former relevant theorems. At last, an
application is presented to illustrate our result. We extend some previous existing results.
Share and Cite
ISRP Style
Xiaoyan Zhang, Fixed points of mixed non-monotone tripled operators in ordered Banach spaces and applications, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 8, 5306--5315
AMA Style
Zhang Xiaoyan, Fixed points of mixed non-monotone tripled operators in ordered Banach spaces and applications. J. Nonlinear Sci. Appl. (2016); 9(8):5306--5315
Chicago/Turabian Style
Zhang, Xiaoyan. "Fixed points of mixed non-monotone tripled operators in ordered Banach spaces and applications." Journal of Nonlinear Sciences and Applications, 9, no. 8 (2016): 5306--5315
Keywords
- Non-monotone tripled operator
- cone theory
- equivalent norms
- fixed points
- Banach spaces.
MSC
References
-
[1]
K. Deimling, Nonlinear functional analysis, Springer-Verlag, Berlin (1985)
-
[2]
D. J. Guo, Semi-ordered method in nonlinear analysis, Shandong Sci. Tech. Press, Jinan, China (2000)
-
[3]
D. J. Guo, V. Lakshmikantham, X. Z. Liu, Nonlinear integral equations in abstract spaces, Mathematics and its Applications, Kluwer Academic Publishers Group, Dordrecht (1996)
-
[4]
J. Harjani, B. López, K. Sadarangani, Fixed point theorems for mixed monotone operators and applications to integral equations, Nonlinear Anal., 74 (2011), 1749--1760
-
[5]
M. A. Krasnoselskiĭ, P. P. Zabreĭko, Geometrical methods of nonlinear analysis, Translated from the Russian by Christian C. Fenske, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], Springer-Verlag, Berlin (1984)
-
[6]
T. Luo, C. X. Zhu, Existence and uniqueness of solutions for (systems of ) mixed non-monotone tripled operator equations in ordered Banach spaces, Adv. Math. (China), 4 (2015), 580--586
-
[7]
W. Shatanawi, B. Samet, M. Abbas, Coupled fixed point theorems for mixed monotone mappings in ordered partial metric spaces, Math. Comput. Modelling, 55 (2012), 680--687
-
[8]
E. Zeidler, Nonlinear Functional Analysis and its Applications, Springer-Verlag, New York (2009)
-
[9]
X. Y. Zhang, Fixed point theorems for a class of nonlinear operators in Banach spaces and applications, Nonlinear Anal., 69 (2008), 536--543
-
[10]
P. G. Zhang, L. S. Liu, Existence and uniqueness of fixed points for mixed non-monotone binary operators in ordered Banach spaces and its applications, (Chinese) Acta Math. Sinica (Chin. Ser.), 53 (2010), 55--60
-
[11]
X. Y. Zhang, J. X. Sun, Existence and uniqueness of solutions for a class of nonlinear operator equations and their applications, (Chinese) Acta Math. Sci. Ser. A Chin. Ed., 25 (2005), 846--851
-
[12]
Z. Zhang, K. Wang, On fixed point theorems of mixed monotone operators and applications, Nonlinear Anal., 70 (2009), 3279--3284
-
[13]
W. T. Zhang, C. X. Zhu, Z. Q. Wu, Existence and uniqueness of solutions for (systems of ) mixed non-monotone binary operator equations, (Chinese) Math. Pract. Theory, 42 (2012), 203--208
-
[14]
Z.-Q. Zhao, Iterative solutions of systems of operator equations in ordered Banach spaces and applications, Non- linear Anal., 26 (1996), 1043--4052
-
[15]
L. Zhao, J. X. Sun, Fixed point theorems of convex-power 1-set-contraction operators in Banach spaces, Fixed Point Theory and Appl., 2012 (2012), 8 pages
-
[16]
Acta Math. Sinica (Chin. Ser.), Iterative solution methods for systems of two binary operator equations, Y. Zheng, L. S. Liu, 49 (2006), 1033--1038
-
[17]
C. X. Zhu, Z. B. Xu, Inequalities and solution of an operator equation, Appl. Math. Lett., 21 (2008), 607--611