A theorem on estimate of pointwise approximation of bounded variation functions defined on by the partial sums of the second Chebyshev-Fourier series is obtained,and this theorem to monotonic type continuous functions is applied.

Several conclusions of bounded variation in infinite integration convergence;

This paper discussed some properties of fuzzy measure,internal measure and fuzzy integration on a normal fuzzy measure space which is subadditive and has bounded variation.

A discussion is made of the continuously sufficient and necessary conditions of the bounded variation f(x)on the closed interval in the paper.

The relation between a class of ordinary differential equations and Kurzweil generalized ordinary differential equations is discussed on weak conditions by using Kurzweil integral,and the theorem of continuous dependence on a parameter of bounded variation solutions for the class of ordinary differential equations is established.

With the aid of Henstock-Kurzweil integral which encompasses the Lebesgue integral,generalized Carathéodory system x =f(t,x)is investigated and the existence theorem of the bounded variation solution for this system is obtained.

In this paper,the variational stability of bounded variation solutions to homogeneous linear ordinary differential equations are disscussed by using Henstock integral and Lyapunov function,the Lyapunov type theories for variation stability and variational-asymptotically stability of bounded variation solutions are established.