- 期刊
CONVERGENCE THEOREMS FOR BANACH SPACE VALUED INTEGRABLE MULTIFUNCTIONS
摘要
In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces L_X^P(Ω) (1 ≤ p ≤ ∞). Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.
被引用紀錄
Lu, K. C. (2001). 一個對於模糊隨機變數的強大數法則和模糊馬亭戈的收斂定理 [master's thesis, National Taiwan Normal University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0021-2603200719120126
延伸閱讀
- Pang, C. T., Naraghirad, E., & Wen, C. F. (2014). Weak Convergence Theorems for Bregman Relatively Nonexpansive Mappings in Banach Spaces. Journal of Applied Mathematics, 2014(), 294-302-531. https://doi.org/10.1155/2014/573075
- Yuan, M., Li, X., Li, X. S., & Liu, J. J. (2012). A Strong Convergence Theorem for Relatively Nonexpansive Mappings and Equilibrium Problems in Banach Spaces. Abstract and Applied Analysis, 2012(), 1234-1245-383. https://doi.org/10.1155/2012/498487
- Wang, Y. H., & Xuan, W. F. (2013). Convergence Theorems for Common Fixed Points of a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces. Abstract and Applied Analysis, 2013(), 366-372-238. https://doi.org/10.1155/2013/259470
- Wang, S., & Kang, S. M. (2013). Strong Convergence Iterative Algorithms for Equilibrium Problems and Fixed Point Problems in Banach Spaces. Abstract and Applied Analysis, 2013(), 931-939-798. https://doi.org/10.1155/2013/619762
- Guan, L., & Li, S. M. (2009). Convergence Theorems for Fuzzy Set-Valued Amart in a Banach Space. International Journal of Intelligent Technologies and Applied Statistics, 2(1), 29-44. https://doi.org/10.6148/IJITAS.2009.0201.03