On strong C-integral of Banach-valued functions defined on \(\mathbb{R}^m\)
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Authors
Dafang Zhao
- College of Science, Hohai University, Nanjing, Jiangsu 210098, P. R. China.
- School of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, P. R. China.
Jingjing Wang
- School of Information Science & Technology, Qingdao University of Science & Technology, Qingdao, Shandong 266061, P. R. China.
Tongxing Li
- LinDa Institute of Shandong Provincial Key Laboratory of Network Based Intelligent Computing, Linyi University, Linyi, Shandong 276005, P. R. China.
- School of Informatics, Linyi University, Linyi, Shandong 276005, P. R. China.
Abstract
In this paper, we define and study the \(C\)-integral and strong \(C\)-integral of functions mapping a compact interval \(I_0\) of \(\mathbb{R}^m\)
into a real Banach space \(X\). We prove that the \(C\)-integral and strong \(C\)-integral are equivalent if and only if \(X\) is finite dimensional.
We also study the relations between the property \(S^*C\) and strong \(C\)-integral.
Share and Cite
ISRP Style
Dafang Zhao, Jingjing Wang, Tongxing Li, On strong C-integral of Banach-valued functions defined on \(\mathbb{R}^m\), Journal of Nonlinear Sciences and Applications, 10 (2017), no. 3, 1221--1227
AMA Style
Zhao Dafang, Wang Jingjing, Li Tongxing, On strong C-integral of Banach-valued functions defined on \(\mathbb{R}^m\). J. Nonlinear Sci. Appl. (2017); 10(3):1221--1227
Chicago/Turabian Style
Zhao, Dafang, Wang, Jingjing, Li, Tongxing. "On strong C-integral of Banach-valued functions defined on \(\mathbb{R}^m\)." Journal of Nonlinear Sciences and Applications, 10, no. 3 (2017): 1221--1227
Keywords
- \(C\)-integral
- property \(S^*C\)
- strong \(C\)-integral.
MSC
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