A Controlled Convergence Theorem for the C-Pettis Integral

A Controlled Convergence Theorem for the C-Pettis Integral

在线阅读下载PDF

导出

摘要 In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We discuss the relationship between the C-Pettis integral and Pettis integral, and prove a controlled convergence theorem for the C-Pettis integral. In this paper, we give the Riemann-type extensions of Dunford integral and Pettis integral, C-Dunford integral and C-Pettis integral. We discuss the relationship between the C-Pettis integral and Pettis integral, and prove a controlled convergence theorem for the C-Pettis integral.

作者 Da Fang ZHAO Bi Wen LI

机构地区 School of Mathematics and Statistics

出处《Journal of Mathematical Research and Exposition》 CSCD 2010年第4期756-760,共5页 数学研究与评论（英文版）

基金 Supported by the Natural Science Foundation of Hubei Province (Grant No.2007ABA124) the Science Foundation of Hubei Normal University (Grant No.2007D41)

关键词 C-integral C-Pettis integral controlled convergence. C-integral C-Pettis integral controlled convergence.

分类号 O174.1 [理学—基础数学]

引文网络
相关文献

参考文献10

1BONGIORNO B. On the minimal solution of the problem of primitives [J]. J. Math. Anal. Appl., 2000, 251(2): 479-487.
2BONGIORNO B, DI PIAZZA L, PREISS D. A constructive minimal integral which includes Lebesgue integrable functions and derivatives [J]. J. London Math. Soc. (2), 2000, 62(1): 117-126.
3DI PIAZZA L. A Riemann-type minimal integral for the classical problem of primitives [J]. Rend. Istit. Mat. Univ. Trieste, 2002, 34(1-2): 143-153.
4GEITZ R F. Pettis integration [J]. Proc. Amer. Math. Soc., 1981, 82(1): 81-86.
5DI PIAZZA L, PREISS D. When do McShane and Pettis integrals coincide? [J]. Illinois J. Math., 2003, 47(4): 1177-1187.
6YE Guoju, AN Tianqing. On Henstock-Dunford and Henstock-Pettis integrals [J]. Int. J. Math. Math. Sci., 2001, 25(7): 467-478.
7LEE P Y, VYBORNY R. Integral: An Easy Approach After Kurzweil and Henstock [M]. Cambridge University Press, Cambridge, 2000.
8ZHAO Dafang, YE Guoju. C-integral and Denjoy-C integral [J]. Commun. Korean Math. Soc., 2007, 22(1): 27-39.
9ZHAO Dafang, YE Guoju. On C-integral of Banach-walued functions [J]. Kangweon-Kyungki J. Math., 2006, 14(2): 169-183.
10ZHAO Dafang, YE Guoju. On strong C-integral of Banach-valued functions [J]. J. Chungcheong Math. Soc 2007, 20(1): 1-10.

1LI Gao-ming.A Convergence Theorem for Set-valued Eventual Supermartingle[J].Chinese Quarterly Journal of Mathematics,2009,24(1):35-39.
2LUO Lai-zhen LI Rong-lu.A separation form of unified convergence theorem[J].Applied Mathematics(A Journal of Chinese Universities),2008,23(1):79-82.
3宋宝瑞.A CONVERGENCE THEOREM ON THE MULTIVARIATE INTERPOLATING RATIONAL FUNCTIONS[J].Journal of Shanghai Jiaotong university(Science),1999,4(2):59-63.
4SergioAmat,SoniaBusquier,VicenteCandela.THIRD ORDER ITERATIVE METHODS WETHOUT USING SECOND FRECHET DERIVATIVE[J].Journal of Computational Mathematics,2004,22(3):341-346.
5HSU Leetsch Charles,徐沥泉.A Convergence Theorem for a Kind of Composite Power Series Expansions[J].Journal of Mathematical Research and Exposition,2008,28(4):850-854.
6Hussein A.H. Salem.FRACTIONAL ORDER BOUNDARY VALUE PROBLEM WITH INTEGRAL BOUNDARY CONDITIONS INVOLVING PETTIS INTEGRAL[J].Acta Mathematica Scientia,2011,31(2):661-672. 被引量：5
7LuYongqing,LiZhongkai.Strong Convergence of the Cesàro Means at the Critical Index of Jacobi Series[J].首都师范大学学报（自然科学版）,1997,18(1):13-16.
8韩丹夫,王兴华.THE ERROR ESTIMATES OF HALLEY'S METHOD[J].Numerical Mathematics A Journal of Chinese Universities(English Series),1997,6(2):231-240.
9王兴华.Convergence of iterations of Euler family under weak condition[J].Science China Mathematics,2000,43(9):958-962. 被引量：5
10JunDeWU,JianWenLUO,ShiJieLU.A Unified Convergence Theorem[J].Acta Mathematica Sinica,English Series,2005,21(2):315-322. 被引量：2

Journal of Mathematical Research and Exposition

2010年第4期

浏览历史

内容加载中请稍等...

A Controlled Convergence Theorem for the C-Pettis Integral

参考文献10

相关作者

相关机构

相关主题

浏览历史