On analytic characteristic functions

Some characteristic properties of analytic functions

In this paper, we consider a class L (λ, μ;φ) of analytic functions f defined in the open unit disk U satisfying the subordination condition that q(z) Df(z) Dλf(z) ≺ φ(z) (λ ∈ N0, μ ≥ 0; z ∈ U), where q(z) = ( z Dλf(z) )μ−2 , D is the Sălăgean operator and φ(z) is a convex function with positive real part in U. We obtain some characteristic properties giving the coefficient inequality, radius a...

Nevanlinna on Analytic Functions

On Bounded Analytic Functions

The objective of this paper is to give an alternative derivation of results on bounded analytic functions recently obtained by Ahlfors [l] and Garabedian [2].1 While it is admitted that the main idea to be used is more in the nature of a lucky guess than of a method, it will be found that the gain in brevity and simplicity of the argument is considerable. As a by-product, we shall also obtain a...

On Non - Analytic Functions

In his retiring presidential address before the American Mathematical Society (December, 1931), E. R. Hedrick gave a resumé of the theory of non-analytic functions of a complex variable.f We propose in the present note to establish, with regard to these functions, some elementary properties that do not appear in the Hedrick report. (In the course of the work, however, some properties considered...

On Sandwich theorems for certain classes of analytic functions

The purpose of this present paper is to derive some subordination and superordination results for certain analytic functions in the open unit disk. Relevant connections of the results, which are presented in the paper, with various known results are also considered.