乘积空间中非线性算子的极大极小不动点定理及迭代法*
Minimal and Maximal Fixed Point Theorems and Iterative Technique for Nonlinear Operators in Product Spaces
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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.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].
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Key words:
- minimal and maximal fixed point /
- coupled fixed point
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[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) -
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