JOURNAL BROWSE
Search
Advanced SearchSearch Tips
THE EXISTENCE RESULTS OF COUPLED QUASI-SOLUTIONS FOR A CLASS OF OPERATOR EQUATIONS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
THE EXISTENCE RESULTS OF COUPLED QUASI-SOLUTIONS FOR A CLASS OF OPERATOR EQUATIONS
Cho, Yeol-Je; He, Guang; Huang, Nan-Jing;
  PDF(new window)
 Abstract
In this paper, by using the semi-order method, two new existence theorems of coupled quasi-solutions for a class of nonlinear operator equations in Banach spaces are proved under some suitable conditions.
 Keywords
cone;partial order;mixed monotone operator;relatively weakly compact set;coupled quasi-solutions;
 Language
English
 Cited by
1.
Coupled Fixed Point Theorems under Weak Contractions, Discrete Dynamics in Nature and Society, 2012, 2012, 1  crossref(new windwow)
2.
Coupled Fixed Point Theorems for Weak Contraction Mappings underF-Invariant Set, Abstract and Applied Analysis, 2012, 2012, 1  crossref(new windwow)
3.
Coupled Coincidence Points in Partially Ordered Cone Metric Spaces with ac-Distance, Journal of Applied Mathematics, 2012, 2012, 1  crossref(new windwow)
4.
Coupled fixed points of weakly F-contractive mappings in topological spaces, Applied Mathematics Letters, 2011, 24, 7, 1185  crossref(new windwow)
5.
Coupled Fixed-Point Theorems for Contractions in Partially Ordered Metric Spaces and Applications, Mathematical Problems in Engineering, 2012, 2012, 1  crossref(new windwow)
 References
1.
S. S. Chang, Y. J. Cho, and H. Y. Zhou, Iterative Methods for Nonlinear Operator Equations in Banach Spaces, Nova Science Publishers, Inc., Huntington, NY, 2002.

2.
Y. Q. Chen and Y. J. Cho, Nonlinear Operator Theory in Abstract Spaces and Applications, Nova Science Publishers, Inc., New York, 2004.

3.
Y. Z. Chen, Fixed points of T-monotone operators, Nonlinear Anal. 24 (1995), no. 8, 1281-1287. crossref(new window)

4.
H. G. Duan and G. Z. Li, The existence of couple minimal-maximal quasi-solutions for a class of nonlinear operator equations, J. Math. (Wuhan) 25 (2005), no. 5, 527-532.

5.
Y. Q. Feng and S. Y. Liu, Solvability of an operator equation in partial ordered space, Acta Math. Sinica (Chin. Ser.) 46 (2003), no. 2, 411-416.

6.
D. J. Guo and V. Lakshmikantham, Nonlinear Problems in Abstract Cone, Academic Press, New York, 1988.

7.
D. J. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal. 11 (1987), no. 5, 623-632. crossref(new window)

8.
G. He, B. S. Lee, and N. J. Huang, Solvability of a new class of mixed monotone operator equations with an application, Nonlinear Anal. Forum 10 (2005), no. 2, 145-151.

9.
N. J. Huang, Y. Y. Tang, and Y. P. Liu, Some new existence theorems for nonlinear inclusion with an application, Nonlinear Funct. Anal. Appl. 6 (2001), no. 3, 341-350.

10.
X. Y. Liu and C. X. Wu, Fixed points of discontinuous weakly compact increasing operators and their applications to initial value problems in Banach spaces, J. Systems Sci. Math. Sci. 20 (2000), no. 2, 175-180.

11.
Y. Syau, Some fixed point theorems of T-monotone operators, J. Math. Anal. Appl. 205 (1997), no. 2, 325-329. crossref(new window)

12.
S. Y. Xu and B. G. Jia, Fixed-point theorems of ${\phi}$ concave-(-${\psi}$) convex mixed monotone operators and applications, J. Math. Anal. Appl. 295 (2004), no. 2, 645-657. crossref(new window)

13.
X. T. Yu, Geometric Theory in Banach Spaces, East China Normal University Press, Shanghai, 1986.

14.
K. M. Zhang, The solution of a nonlinear nonmonotone operator equation, Acta Math. Sci. (Chinese) 18 (1998), no. 2, 164-168.

15.
K. M. Zhang and X. J. Xie, Solution and coupled minimal-maximal quasi-solutions of nonlinear non-monotone operator equations in Banach spaces, J. Math. Res. Exposition 23 (2003), no. 1, 47-52.

16.
Z. Zhou and Z. X. Yu, Fixed point theorems for mixed monotone operators and their applications, Gaoxiao Yingyong Shuxue Xuebao Ser. A 12 (1997), no. 3, 347-352.