Let f(w) be an analytic and univalent function in a convex domain D. Sharp bounds on the estimates of |f(n)(w)/f'(w)| are found for all w in D and 2≤n≤8. These estimates generalize several known results.
Let X be a real Banach space which is both p uniformly convex and uniformly smooth, T:D(T)X be a Lipschitzian m accretive operator. Under the natural setting that the domain of T , D(T) is a proper subset of X ,method of approximating a solution of the equation x+Tx=f is studied. The results extend several known results.
in this paper,we first established three differential identity,and then discussed the oscillation comparison theorems of prepared solutions and derivative function of prepared solutions forsystem (P(t)Y') ' + Q(t)Y= 0,and grneralized some known results.
Chapter 3: In this chapter, the author is to study the existence theorems of random solutions for random semi-closed 1-set contraction operators equation A(co,x)=ux (u>l) in different border condition and obtains some new results.
We also use known results about canonical bases forUq2 to get a new proof of recurrent formulas for KL polynomials for maximal parabolic subgroups (geometrically, this case corresponds to Grassmannians), due to Lascoux-Schützenberger and Zelevinsky.
These estimates not only improve, but also extend some known results in the related topics.
The exact soliton solutions are given and the relation between this condition and the known results in the literature is also discussed.
In addition, some known results about the Cartesian products of two directed cycles are also deduced.
In this paper, a new criterion of the non-existence of periodic solutions for a generalized liénard system is given, which generalizes and extends some known results of Sugie et al.