On the asymptotic formulae of approximation of unbounded continuous functions;

By using multiplier-enlargement,the asymptotic estimation of approximation of unbounded continous functions with positive linear operaters is discussed, with general asymptotic formulae given.

By using of the method of multiplier-enlargement, discusses the asymptotic estimation of approximation for unbounded continuous functions of several variables by linear positive operators defined on k-dimensional Euclidean space, and gives general asymptotic formulae.

Singularly perturbed boundary value problems for a class of third order nonlinear differential equations :εx\+=f(t,x,x\+′,x\+″,ε),x(0)=A ,x\+′(0)=x\+′(1),x\+″(0)=x\+″(1),is studied by upper and lower solutions, the existence and asymptotic estimates of solution are obtained.

The periodic boundary value problem on integral differential equation of Volterra mode bearing minor parameter in a second order derivative term is studied,namely,εu″=f(t,u,Tu,(ε)u′,ε),u(0)=u(1),u′(0)=u′(1),\%thus, both the existence and the asymptotic estimate of solution to the problem are found out.

An asymptotic estimate for integral remainder of Simpson formula and a consequence of inverse problem of Simpson formula are given in this article.

By using WZ method, the asymptotic estimates for some special cases of a kind of combinatorial sum were obtained, then some general results were conjectured from them and proved by using analytic method.

The existence result and the asymptotic estimates of the solution in the maximum norm are examined by means of some fixed point theorems.

The existence and asymptotic estimates of solution for nonlinear boundary value problem of Volterra type integro-differential-difference equation by means of differential inequality theories is studied.