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On a generalization of close-to-convex functions

Swadesh Kumar Sahoo, Navneet Lal Sharma (2015)

Annales Polonici Mathematici

The paper of M. Ismail et al. [Complex Variables Theory Appl. 14 (1990), 77-84] motivates the study of a generalization of close-to-convex functions by means of a q-analog of the difference operator acting on analytic functions in the unit disk 𝔻 = {z ∈ ℂ:|z| < 1}. We use the term q-close-to-convex functions for the q-analog of close-to-convex functions. We obtain conditions on the coefficients of power series of functions analytic in the unit disk which ensure that they generate functions in...

On an entire function represented by multiple Dirichlet series

Lakshika Chutani (2021)

Mathematica Bohemica

Consider the space L of entire functions represented by multiple Dirichlet series that becomes a non uniformly convex Banach space which is also proved to be dense, countable and separable. Continuing further, for the given space L the characterization of bounded linear transformations in terms of matrix and characterization of linear functional has been obtained.

On Bloch functions and gap series.

Daniel Girela (1991)

Publicacions Matemàtiques

Kennedy obtained sharp estimates of the growth of the Nevanlinna characteristic of the derivative of a function f analytic and with bounded characteristic in the unit disc. Actually, Kennedy's results are sharp even for VMOA functions. It is well known that any BMOA function is a Bloch function and any VMOA function belongs to the little Bloch space. In this paper we study the possibility of extending Kennedy's results to certain classes of Bloch functions. Also, we prove some more general results...

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