用Ruscheweyh导数刻画的解析函数新子类

引进并研究用Ruscheweyh导数定义的解析函数类Sk,[λα,β,ρ].结合算子理论导出类中函数的积分表达式、偏差定理,讨论类中函数的半径问题和Hadamard卷积性质.     

Some properties of certain meromorphic close-to-convex functions

In the present paper, we introduce and investigate a certain subclass of meromorphic close-to-convex functions. Such results as coefficient inequalities, convolution property, distortion property and radius of meromorphic convexity are derived.     

Hadamard products with power functions and multipliers of Hardy spaces

We consider Hadamard products of power functions P(z)=(1−z)^−b with functions analytic in the open unit disk in the complex plane, and an integral representation is obtained when 0<Reb<2. Let where μ is a complex-valued measure on the closed unit disk Such sequences are shown to be multipliers of H^p for 1?p?∞. Moreover, if the support of μ is contained in a finite set of Stolz angles with vertices on the unit circle, we prove that {μ_n} is a multiplier of H^p for every p>0. When the support of μ is [0,1] we get the multiplier sequence which provides more concrete applications. We show that if the sequences {μ_n} and {ν_n} are related by an asymptotic expansion

     

On the convolution and subordination of convex functions

In this work we present some new results on convolution and subordination in geometric function theory. We prove that the class of convex functions of order α is closed under convolution with a prestarlike function of the same order. Using this, we prove that subordination under the convex function order α is preserved under convolution with a prestarlike function of the same order. Moreover, we find a subordinating factor sequence for the class of convex functions. The work deals with several ideas and techniques used in geometric function theory, contained in the book Convolutions in Geometric Function Theory by Ruscheweyh (1982).     

The maximal ideal space of with respect to the Hadamard product

It is shown that the space of all regular maximal ideals in the Banach algebra with respect to the Hadamard product is isomorphic to The multiplicative functionals are exactly the evaluations at the -th Taylor coefficient. It is a consequence that for a given function in and for a function holomorphic in a neighborhood of with and for all the function is in

     

Starlike and close-to-convex functions defined by differential inequalities

We present new sufficient conditions for an analytic function to be close-to-convex and starlike, respectively. These conditions are easy to apply and can be used to obtain functions in these classes.     

用Choi-Saigo-Srivastava算子定义的解析函数新子类

本文研究了用Choi-Saigo-Srivastava算子定义的一类解析函数.利用分析的方法和算子理论得到类中函数的积分表达式,偏差定理,卷积性质和半径问题.所得结果推广一些作者的相关结果.     

Weak subordination for convex univalent harmonic functions

For two complex-valued harmonic functions f and F defined in the open unit disk Δ with f(0)=F(0)=0, we say f is weakly subordinate to F if f(Δ)⊂F(Δ). Furthermore, if we let E be a possibly infinite interval, a function with f(⋅,t) harmonic in Δ and f(0,t)=0 for each t∈E is said to be a weak subordination chain if f(Δ,t₁)⊂f(Δ,t₂) whenever t₁,t₂∈E and t₁<t₂. In this paper, we construct a weak subordination chain of convex univalent harmonic functions using a harmonic de la Vallée Poussin mean and a modified form of Pommerenke's criterion for a subordination chain of analytic functions.     

近于凸函数新子类的偏差定理和卷积性质

引进了近于凸函数的新子类.利用从属关系得到了偏差定理和卷积性质.所得结果推广了一些作者的相关结果,并得到有趣的新结果.     

Hadamard type inequality for quasiconvex functions in higher dimensions

In this article we study a Hadamard type inequality for nonnegative evenly quasiconvex functions. The approach of our study is based on the notion of abstract convexity. We also provide an explicit calculation to evaluate the asymptotically sharp constant associated with the inequality over a unit square in the two-dimensional plane.     

Subordination Results for p-Valent Meromorphic Functions Associated with a Linear Operator

In this paper, by making use of the Hadamard products, we obtain some subordination results for certain family of meromorphic functions defined by using a new linear operator.     

On generalized Euler constants and Schlömilch-Lemonnier type inequalities

We study the monotonicity properties of certain sequences involving generalized Euler constants and their connections with generalized Schlömilch-Lemonnier type inequalities.     

一类亚纯多叶星象函数的子族

本文研究了一类亚纯多叶星象函数的子族(?)_p(β,λ).利用分析的方法与技巧,得到了函数族(?)_p(β,λ)的系数估计、邻域与部分和性质及一些包含关系,所得结果推广了相关作者的一些成果.     

New inequalities for the minimum eigenvalue of M-matrices

Some new inequalities for the minimum eigenvalue of M-matrices are established. These inequalities improve the results in [G. Tian and T. Huang, Inequalities for the minimum eigenvalue of M-matrices, Electr. J. Linear Algebra 20 (2010), pp. 291–302].     

New inequalities from classical Sturm theorems

Inequalities satisfied by the zeros of the solutions of second-order hypergeometric equations are derived through a systematic use of Liouville transformations together with the application of classical Sturm theorems. This systematic study allows us to improve previously known inequalities and to extend their range of validity as well as to discover inequalities which appear to be new. Among other properties obtained, Szegő's bounds on the zeros of Jacobi polynomials for , are completed with results for the rest of parameter values, Grosjean's inequality (J. Approx. Theory 50 (1987) 84) on the zeros of Legendre polynomials is shown to be valid for Jacobi polynomials with |β|1, bounds on ratios of consecutive zeros of Gauss and confluent hypergeometric functions are derived as well as an inequality involving the geometric mean of zeros of Bessel functions.     

Starlikeness of Hadamard product of certain analytic functions

An interesting criterion was given by Lashin (A.Y. Lashin, Some convolution properties of analytic functions, Appl. Math. Lett. 18 (2005) 135–138) to be starlike for convolution of analytic functions f, g such that Re[f^′(z)],Re[g^′(z)]β,,β<1 in the unit disc U. In this paper we shall improve this criterion.     

Properties of Some Families of Meromorphic Multivalent Functions Associated with Generalized Hypergeometric Functions

We introduce and study two subclasses ?_([α_1])(A, B, λ) and ?_([α_1])~+ (A, B, λ) of meromorphic p-valent functions defined by certain linear operator involving the generalized hypergeometric function. The main object is to investigate the various important properties and characteristics of these subclasses of meromorphically multivalent functions. We extend the familiar concept of neighborhoods of analytic functions to these subclasses. We also derive many interesting results for the Hadamard products of functions belonging to the class ?_([α_1])~+(α, β, γ, λ).