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http://dx.doi.org/10.14403/jcms.2011.24.3.8

CHARACTERIZING CONVERGENCE CONDITIONS FOR THE Mα-INTEGRAL  

Garces, Ian June Luzon (Department of Mathematics Ateneo de Manila University)
Racca, Abraham Perral (Mathematics and Physics Department Adventist University of the Philippines)
Publication Information
Journal of the Chungcheong Mathematical Society / v.24, no.3, 2011 , pp. 469-480 More about this Journal
Abstract
Park, Ryu, and Lee recently defined a Henstock-type integral, which lies entirely between the McShane and the Henstock integrals. This paper presents two characterizing convergence conditions for this integral, and derives other known convergence theorems as corollaries.
Keywords
$M_{\alpha}$-integral; $M_{\alpha}$-convergence; equi-integrability;
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  • Reference
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2 J. M. Park, H. W. Ryu and H. K. Lee, The $M_{\alpha}$-integral, J. Chungcheong Math. 23 (2010), no. 1, 99-108.
3 J.M. Park, D.H. Lee, J.H. Yoon and H.K. Lee, The integration by parts for the $M_{\alpha}$integral, J. Chungcheong Math. 23 (2010), no. 4, 861-870.