The Solution of Binary Nonlinear Operator Equations with Applications

Author(s)
Baomin Qiao

ABSTRACT

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.

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.

B. Qiao, "The Solution of Binary Nonlinear Operator Equations with Applications,"

References

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[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.

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[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.