Meromorphic univalent functions in an annulus

We consider the integral means for the class of functions which are meromorphic and univalent in an annulus.     

Landau problem for the class of functions that are regular in an annulus

The classical result of Landau, establishing the radius of the largest circle, in which, for any function f(z)R, where R is the class of regular functions w=f(z)=z+c₂z²+..., in¦z¦<1, ¦f(z)¦相似文献   

Distortion theorems for univalent meromorphic functions on an annulus

We apply the capacity and symmetrization methods to distortion theorems for analytic functions in an annulus. We show that the classical Teichmüller estimate for the capacity of a doubly-connected domain yields a series of the already known and new inequalities for univalent functions. In particular, we supplement the results of Grötzsch, Duren, and Huckemann. Using the dissymmetrization of condensers we establish sharp estimates for local distortion and the distortion of level curves in n ≥ 2 symmetric directions. In terms of Robin functions we give an analog of the Nehari inequality: some general distortion theorem for several points taking into account the boundary behavior of the function and describing the cases of equalities. As a corollary we give analogs of some inequalities of Solynin, Pommerenke, and Vasil’ev that were obtained previously for univalent and bounded functions in a disk. We prove a distortion theorem that involves the Schwarzian derivatives at symmetric points on the unit circle.     

Quasi-Hadamard product of certain univalent functions

The author improves some recent results due to Shigeyoshi Owa (Tamkang J. Math., 14 1983, 15–21) concerning the quasi-Hadamard product of certain starlike and convex univalent functions.     

Proof of the bieberbach conjecture for a certain class of univalent functions

In the following we prove that for a given univalent function such that |a ₂| <0.867, |a _n |≦n for eachn. The method of proof is closely related to Milin’s method.     

A new class of Salagean-type harmonic univalent functions

We define and investigate a new class of Salagean-type harmonic univalent functions. We obtain coefficient conditions, extreme points, distortion bounds, convex combination and radii of convex for the above class of harmonic univalent functions.     

A rotation theorem in the class of bounded univalent functions

Let S_M, M > 1, be the class of functionsf(z) which are regular and univalent in the disk ¦z¦ < 1 and satisfy the conditionsf(0) = 0,f'(0) = 1, and ¦f(z)¦ < M. In the present note we will obtain an exact estimate for the argument of the derivative of a function of the class S_M.     

A certain class of gammamorphic functions

Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 41, No. 11, pp. 1561–1563, November, 1989.     

A rotation theorem for the class of univalent p-symmetric functions

Exact estimates are obtained for the argument of the derivative on the class of all univalent holomorphic p-symmetric functions in the unit disk.Translated from Matematicheskie Zametki, Vol. 10, No. 2, pp. 239–242, August, 1971.     

Integral representation of a class of univalent functions

We refine and generalize a result of V. A. Zmorovich on the integral representation of a class of univalent functions which are convex in some direction. We prove that all function of the class being considered can be approximated by a Schwarz-Christoffel integral of a special form belonging to the same class.Translated from Matematicheskii Zametki, Vol. 19, No. 1, pp. 41–48, January, 1976.     

Some relations between certain inequalities concerning analytic and univalent functions

By making use of the well-known assertions in [S.S. Miller, P.T. Mocanu, Differential Subordinations, Theory and Applications, Marcel Dekker, New York-Basel, 2000] and [M. Nunokawa, On the order of strongly starlikeness of strongly convex functions, Proc. Japan Acad. Ser. A Math. Sci. 69 (7) (1993) 234–237], several useful results of certain inequalities dealing with analytic and univalent functions are obtained and then certain consequences of them are also indicated.