Share This Article:

The Solution of Binary Nonlinear Operator Equations with Applications

Abstract Full-Text HTML XML Download Download as PDF (Size:139KB) PP. 1237-1241
DOI: 10.4236/am.2013.49167    4,113 Downloads   5,636 Views  
Author(s)    Leave a comment


In this paper, the existence and uniqueness of solution systems for some binary nonlinear operator equations are discussed by using cone and partially order theory and monotone iteration theory, and the iterative sequences which converge to solution of operator equations and error estimates for iterative sequences are also given. Some corresponding results are improved and generalized. Finally, the applications of our results are given.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

B. Qiao, "The Solution of Binary Nonlinear Operator Equations with Applications," Applied Mathematics, Vol. 4 No. 9, 2013, pp. 1237-1241. doi: 10.4236/am.2013.49167.


[1] D.-J. Guo and V. Lakshmikantham, “Coupled Fixed Points of Nonlinear Operators with Applications,” Nonlinear Analysis, Vol. 11, No. 5, 1987, pp. 623-632. doi:10.1016/0362-546X(87)90077-0
[2] Y. Sun, “A Fixed Point Theorem for Mixed Monotone Operators with Applications,” Journal of Mathematical Analysis and Applications, Vol. 21, No. 6, 1991, pp. 240-252.
[3] Q.-Z. Zhang, “Contraction Mapping Principle of Mixed Monotone Mapping and Applications,” Henan Science, Vol. 18, No. 2, 2000, pp. 121-125.
[4] J.-X. Sun and L.-H. Liu, “Iterative Solutions for Nonlin ear Operator Equation with Applications,” Acta Mathe matica Scientia, Vol. 13, No. 3, 1993, pp. 141-145.
[5] Q.-Z. Zhang, “Iterative Solutions of Ordering Symmetric Contraction Operator with Applications,” Journal of En gineering Mathematics, Vol. 17, No. 2, 2000, pp. 131-134.
[6] X.-L. Yan, “The Fixed Point Theorems for Mixed Mono tone Operator with Application,” Mathematical Applica tion, Vol. 4, No. 4, 1991, pp. 107-114.

comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.