乘积空间中非线性算子的极大极小不动点定理及迭代法<sup>*</sup>

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乘积空间中非线性算子的极大极小不动点定理及迭代法^*

基金项目: * 国家自然科学基金资助项目

摘要: 本文研究了乘积空间中非线性算子的极大极小不动点和迭代法.作为我们结果的推论,一些耦合不动点定理被获得、它们推广了由郭大钧和Lankshmikantham获得的耦合不动点定理.(见Nonlinear Anal、11(1986),623-632)和由兰在[4]、[6]中获得的结果.
- 极大极小不动点 /
- 耦合不动点
Abstract: In this paper, we study minimal and maximal fixed point theorems and iterative technique for nonlinear operators in product spaces. As a corollary of our result, some coupled fixed point theorems are obtained, which generalize the coupled fixed point theorems obtained by Guo Da-jun and Lankshmikantham^[2] and the results obtained by Lan in [4] and [6].
- minimal and maximal fixed point /
- coupled fixed point

[1]	Ladde, G. S., V. Lakshmikantham and A. S. Vatsala, Monotone Iterative techniques for nonlinear differential equations. Pitman (1985).
[2]	Guo Da-jun and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal., 11 (1987), 623-632.
[3]	Martin, R. H., Nonlinear Operators and Differential Equation, Wiley, New York (1976).
[4]	兰坤泉.混合单调映象、增映象和不动点,四川师范大学学报.(待发表)
[5]	余庆余,凝聚映象的不动点定理,数学学报.24(1981), 430-435,
[6]	兰坤泉,混含单调凝聚映象的藕合不动点,四川师范大学学报.(待发表)