Norm estimates for the Alexander transforms of convex functions of order alpha

The hyperbolic sup norm of the pre-Schwarzian derivative of a locally univalent function on the unit disk measures the deviation of the function from similarities. We present sharp norm estimates for the Alexander transforms of convex functions of order α, 0?α<1.     

Certain family of integral operators preserving subordination and superordination

We obtain subordination, superordination and sandwich-preserving new theorems for certain integral operators defined on the space of normalized analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also derived, and the results generalize some recently ones.     

Univalence criterion for meromorphic functions and Loewner chains

The object of the present paper is to obtain a more general condition for univalence of meromorphic functions in the U^∗. The significant relationships and relevance with other results are also given. A number of known univalent conditions would follow upon specializing the parameters involved in our main results.     

On some applications of a subordination theorem

The main object of the present paper is to show some interesting relations for certain class of analytic functions by using subordination theorem.     

Starlikeness and subordination properties of a linear operator

In this paper, we introduce a new class of p-valent analytic functions defined by using a linear operator L_k^α. For functions in this class H_k^α(p,λh) we estimate the coefficients. Furthermore, some subordination properties related to the operator L_k^α are also derived.     

Killing and subordination

Given the one-to-one correspondence between nearly Borel right processes and non-symmetric Dirichlet forms, we prove in the present paper that the killing transform of Markov processes is equivalent to strong subordination of the respective Dirichlet forms and give a characterization of so-called bivariate smooth measures.

     

Briot-Bouquet differential superordinations and sandwich theorems

Briot-Bouquet differential subordinations play a prominent role in the theory of differential subordinations. In this article we consider the dual problem of Briot-Bouquet differential superordinations. Let β and γ be complex numbers, and let Ω be any set in the complex plane C. The function p analytic in the unit disk U is said to be a solution of the Briot-Bouquet differential superordination if

     

Circular symmetrization,subordination and arclength problems on convex functions

We study the class of univalent analytic functions f in the unit disk of the form satisfying where Ω will be a proper subdomain of which is starlike with respect to . Let be the unique conformal mapping of onto Ω with and and . Let denote the arclength of the image of the circle , . The first result in this paper is an inequality for , which solves the general extremal problem , and contains many other well‐known results of the previous authors as special cases. Other results of this article cover another set of related problems about integral means in the general setting of the class .     

一致星象和凸象超几何函数的一些性质

介绍了(高斯)超几何函数属于一致星象函数和一致凸函数的某些子类的一些性质.还考虑了与超几何函数相关的算子.     

Loewner chains associated with the generalized Roper-Suffridge extension operator on some domains

In this paper, we consider the generalized Roper-Suffridge extension operator defined by

     

Convex -closures versus convex norm-closures in dual Banach spaces

A subset Y of a dual Banach space X^* is said to have the property (P) if for every weak^*-compact subset H of Y. The purpose of this paper is to give a characterization of the property (P) for subsets of a dual Banach space X^*, and to study the behavior of the property (P) with respect to additions, unions, products, whether the closed linear hull has the property (P) when Y does, etc. We show that the property (P) is stable under all these operations in the class of weak^* -analytic subsets of X^*.     

Some starlikeness criterions for analytic functions

We determine a condition on M, α, λ and μ for which

     

Löwner chains and a subclass of biholomorphic mappings

In this paper, we give characterization of almost starlike functions of order α (respectively almost starlike mappings of order α) on the unit disc in C (respectively the unit ball in a finite-dimensional complex Banach space) in terms of Löwner chains. Furthermore, using the properties of Löwner chains, we can easily prove that two classes of generalized Roper-Suffridge extension operators preserve almost starlikeness of order α on two important classes of Reinhardt domains in Cn, respectively.     

Growth theorems and coefficient bounds for univalent holomorphic mappings which have parametric representation

Let B be the unit ball in Cn with respect to an arbitrary norm and let f(z,t) be a g-Loewner chain such that e−tf(z,t)−z has a zero of order k+1 at z=0. In this paper, we obtain growth and covering theorems for . Moreover, we consider coefficient bounds and examples of mappings in .     

On some applications of the Briot-Bouquet differential subordination

Recently Srivastava et al. [J. Dziok, H.M. Srivastava, Certain subclasses of analytic functions associated with the generalized hypergeometric function, Integral Transforms Spec. Funct. 14 (2003) 7-18; J. Dziok, H.M. Srivastava, Classes of analytic functions associated with the generalized hypergeometric function, Appl. Math. Comput. 103 (1999) 1-13; Y.C. Kim, H.M. Srivastava, Fractional integral and other linear operators associated with the Gaussian hypergeometric function, Complex Var. Theory Appl. 34 (1997) 293-312] introduced and studied a class of analytic functions associated with the generalized hypergeometric function. In the present paper, by using the Briot-Bouquet differential subordination, new results in this class are obtained.     

Geometric Tomography of Convex Cones

The parallel X-ray of a convex set K⊂ℝ ⁿ in a direction u is the function that associates to each line l, parallel to u, the length of K∩l. The problem of finding a set of directions such that the corresponding X-rays distinguish any two convex bodies has been widely studied in geometric tomography. In this paper we are interested in the restriction of this problem to convex cones, and we are motivated by some applications of this case to the covariogram problem. We prove that the determination of a cone by parallel X-rays is equivalent to the determination of its sections from a different type of tomographic data (namely, point X-rays of a suitable order). We prove some new results for the corresponding problem which imply, for instance, that convex polyhedral cones in ℝ³ are determined by parallel X-rays in certain sets of two or three directions. The obtained results are optimal.     

四元数矩阵凸函数及其不等式

本文推广复矩阵凸函数及其性质到四元数体上矩阵，并且得到关于四元数矩阵凸函数的一些不等式．