随机集值映射的不动点定理及其应用
Fixed Point Theorems of Random Set-Valued Mappings and Their Applications
-
摘要: 本文对随机集值映射和随机集值映射组证明了几个新的随机不动点定理,然后我们给出了所得结果对非线性随机积分方程组和随机微分方程组的某些应用。我们的结果改进和推广了[4~7,9,11~17]中的若干最近结果。Abstract: In this paper, first we show several new random fixed point theorems for random set-valued mappings and for a system of random set-valued mappings. Then, some applications of our results are given for the existence and uniqueness of random solution for a system of nonlinear random integral and differential equations. Our theorems improved and generalize many recent findings in [4-7, 9, 11-17].
-
[1] Bharucha-Reid, A. T., Random Integral Equations, Press, New York,(1972). [2] Bharucha-Reid, A. T., Bull. Amer. Math. Soc., 82(1976), 641-657. [3] Tsokos, C. P. and W. J. Padgett, Random Integral Equations with Applications in Life and Engineering, Press, New York,(1974). [4] Singh, K. L. and J. H. M. Whitfield; Math. Japonica, 27(1982), 117-124. [5] Czerwik, S.,Proc. Amer. Math. Soc., 55(1976), 136-139. [6] Itoh, S., Pacific J. Math., 68(1977), 85-90. [7] Andrus, G. F. and T. Nishiura, Nonlinear Anal., TMA 3(1979), 65-72. [8] Himmelberg, C. J., Fundam. Math., 87(1975), 53-72. [9] 王梓坤,数学进展.(1962), 45-71 [10] Kuratowski, K. and C. Ryll-Nardzewski, Bull. Acad. Poion. Sci. Ser. Sci. Math.Astronom Phys., 13(1965), 397-403. [11] Matkowski, J., Bull. Acad. Poion. Sci., 21(1973). [12] Matkowski, J., Dissertations Math.(Rozprawy Mat.), 27(1975), 1-68. [13] Castaing, C. and M. Valadier, Convex Analysis and Measurable Multifunctions, Springer-Verlag,(1977), 580. [14] 丁协平.数学进展,12,2(1983). [15] 刘作述、陈绍仲.科学通报,2(1982), 1161-1162. [16] Keich, S,,Boll, U n, Mat, Ital,,4(1972),26-42. [17] iseki, K.,Rend Sem. Mat, Univ Padova,,53 (1975),15-19.
点击查看大图
计量
- 文章访问数: 1668
- HTML全文浏览量: 77
- PDF下载量: 721
- 被引次数: 0