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.
Garces, I., & Racca, A. (2011). Characterizing Convergence Conditions for the Mα-Integral. Journal of the Chungcheong Mathematical Society, 24(3), 469-480.