At first,we can transform the ordinary differential equation of original function into the algebraic equation of image function,or transform the partial differential equation into ordinary differential equation by Laplace transforms method.
用Laplace变换法可把原函数所遵从的常系数微分方程变成像函数所遵从的代数方程来进行求解;把偏微分方程变成常系数微分方程,然后进行求解。
Next by using this differential inequality,some new sufficient conditions for starlike functions and close-to-convex functions with respect to k-symmetric points are obtained,which generalize some existing results.
首先建立了一个微分不等式,然后利用这一微分不等式得到一些新的星像函数和关于k折对称点近于凸函数的充分条件,也推广了一些已有的结果。
Using this operator,a subclass Τ_(n+p-1)(η;A,B)() of p-valent analytic functions is investigated,the necessary and sufficient condition of f(z) belonging to Τ_(n+p-1)(η;A,B)() is obtained,some relationships are preserved under the integral operator F_(λ,p),the radius of starlike functions and convex functions are also considered.
用H adam ard积(或卷积)定义线性算子In+p-1,并利用算子In+p-1研究在单位圆内解析的p叶函数类Τn+p-1(η;A,B),给出函数f(z)属于类Τn+p-1(η;A,B)的充分必要条件,考虑了函数在积分算子Fλ,p作用下的保持关系,还考虑了星像函数和凸像函数的半径。
Some subclasses R(m,λ,μ,α) of starlike functions are introduced.
引入了星像函数类的一些子类R(m,λ,μ,α),应用微分不等式和微分从属方法讨论了它们的包含关系、系数估计和覆盖定理,得到一些精确的结果。
This paper studies a new subcategory S* of univalent functions, which is the generalization of star-like functions.
研究单叶函数的一个新子族S觹熏它是星像函数的拓广。
Using this operator,a subclass Τ_(n+p-1)(η;A,B)() of p-valent analytic functions is investigated,the necessary and sufficient condition of f(z) belonging to Τ_(n+p-1)(η;A,B)() is obtained,some relationships are preserved under the integral operator F_(λ,p),the radius of starlike functions and convex functions are also considered.
用H adam ard积(或卷积)定义线性算子In+p-1,并利用算子In+p-1研究在单位圆内解析的p叶函数类Τn+p-1(η;A,B),给出函数f(z)属于类Τn+p-1(η;A,B)的充分必要条件,考虑了函数在积分算子Fλ,p作用下的保持关系,还考虑了星像函数和凸像函数的半径。