Extreme problems in the space of meromorphic functions of finite order in the half plane. II

The extremal problems in the space of meromorphic functions of order $\rho>0$ in upper half-plane are studed.The method for studying is based on the theory of Fourier coefficients of meromorphic functions. The concept of just meromorphic function of order $\rho>0$ in upper half-plane is introduced. Using Lemma on the P\'olya peaks and the Parseval equality, sharp estimate from below of the upper limits of relations Nevanlinna characteristics of meromorphic functions in the upper half plane are obtained.

Subordination and superordination results for the family of Jung-Kim-Srivastava integral operators

In this paper, we derive some subordination and superordination results associated with the family of Jung-Kim-Srivastava integral operators defined on the space of meromorphic functions. Several sandwich-type results are also obtained. 2010 Mathematics Subject Classifications. Primary 30C45; Secondary 30C80. .

A Class of Nonlinear Integral Operators Preserving Double Subordinations

The purpose of the present paper is to investigate some subordination- and superordination-preserving properties of certain integral operators defined on the space of meromorphic functions in the punctured open unit disk. The sandwich-type theorem for these integral operators is also considered.

On Joint Distribution of General Dirichlet Series

In the paper a joint limit theorem in the sense of the weak convergence in the space of meromorphic functions for general Dirichlet series is proved under weaker conditions as in [1].

The locally convex topology on the space of meromorphic functions

We give a positive answer to a question of Horst Tietz. A theorem of his that is related to the Mittag-Leffler theorem looks like a duality restult under some locally convex topology on the space of meromorphic functions. Tietz has posed the problem of finding such a topology. It is shown that a topology introduced by Holdguün in 1973 solves the problem. The main tool in the study of this topology is a projective description of it that is derived here. We also argue that Holdgrün's topology is the natural locally convex topology on the space of meromorphic functions.