动态规划中提出的一类泛函方程组公共解和重合解的存在性定理
Some Existence Theorems of Common and Coincidence Solutions for a Class of Functional Equations Arising in Dynamic Programming
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摘要: 本文讨论了动态规划中提出的一类更一般的泛函方程组公共解和重合解的存在性问题.本文的结果不仅包含引文[6,7]中相应结果为特例,而且也对引文[2～5]在讨论动态规划的原理和模型时所提出的一类新型的泛函方程给出解的存在性条件.Abstract: Same existence theorems of common and coincidence solutions for a class of more general systems of functional equations arising in dynamic programming are shown. The results presented in this paper not only contain the corresponding results of [6,7] as special cases, hut also give an existence theorem of solutions for a class of functional equations suggested by Wang[2,5] recently.
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[1] Bellman R. and E. S. Lee, Functional equations in dynamic programming, Aegoations Math.,17(1978). 1-18. [2] Wang Chung-lie, The principle and models of dynamic programming (Ⅱ), J. Math Anal. Appl.,135(1988). 268-283. [3] wang Chung-lie, The principle and models of dynamic programming(Ⅲ),J. Math. Anal.Appl., 135(1988). 284-296. [4] Wang Chung-lie,Theprinciple and models of dynamic programming (IV), J. Math Anal. Appl.,137(1989), 148-160. [5] Wang Chung-lie, The principle and models ofdynamic programming (V), J. Math. Anal. Appl.137 (1989), 161-167. [6] Bhakta. P. C. and Sumitra Mitra, Some existence theorems for functional equations arising in dynamic programming, J. Math.,Anal. Appl. 98(1984), 348-366 [7] Baskaran, R. and P. V. Subrahmanyam, A note on the solution of a class of functional equations, Applicable Artalosis, 22(1986). 235-241. [8] 张石生,《不动点理论及应用》,重庆出版社(1984). [9] Chang Shih-sen (Zhang Shi-Sheng), On common fixed point theorem for a family of Φ-contraction mappings, Math. Japonica, 29(1984), 527-536. [10] Zhang Shi-sheng, Fixed point theorems for generalized Meir-Keeler type mappings, J. Sichuan Univ..Nutural Sci. Edition. 2(1983), 17-23. -
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