The Henstock Integral Of Banach-Valued Functions And Discontinuous System Of Differential Equations

The paper mainly discusses the following questions using with the theory of Hen-stock integral. The relationship between Henstock integral and Henstock-Pettis integral by the properties of Henstock integral of Banach-valued functions is founded, and necessary and sufficient condition for the existence of Henstook-Dunford integral is discussed. Some complete characterization of the primitives of a strong Henstock integrable function in Banach space are given. The properties of Henstock equi-integrability of Banach-valued functions are diccussed, and some convergence theorems of the Henstock integral of Banach-valued functions are given. Lastly, the existence, uniqueness and continuous dependence on a prameter theorems for differential equation are proved.