Some argument inequalities for certain analytic functions

For analytic functions f(z) in the open unit disk U and convex functions g(z) in U, Nunokawa et al. [NUNOKAWA, M.—OWA, S.—NISHIWAKI, J.—KUROKI, K.—HAYAMI, T: Differential subordination and argumental property, Comput. Math. Appl. 56 (2008), 2733–2736] have proved one theorem which is a generalization of the result [POMMERENKE, CH.: On close-toconvex analytic functions, Trans. Amer. Math. Soc. 114 (1965), 176–186]. The object of the present paper is to generalize the theorem due to Nunokawa et al..     

Some properties for certain classes of univalent functions defined by differential inequalities

Let A be the space of functions analytic in the unit disk D = {z:|z| 1}.Let U denote the set of all functions f ∈ A satisfying the conditions f(0) = f'(0)-1 = 0 and|f'(z)(z/f(z))~2-1|1(|z|1).Also,let Ω denote the set of all functions f ∈ A satisfying the conditions f(0) = f'(0)-1 = 0and|zf'(z)-f(z)|1/2(|z|1).In this article,we discuss the properties of U and Ω.     

Coefficient inequalities for univalent starlike functions

Let A be the class of analytic functions in the unit disk $\mathbb{D}$ with the normalization f(0) = f′(0) ? 1 = 0. In this paper the authors discuss necessary and sufficient coefficient conditions for f ∈ A of the form $$\left( {\frac{z} {{f(z)}}} \right)^\mu = 1 + b_1 z + b_2 z^2 + \ldots$$ to be starlike in $\mathbb{D}$ and more generally, starlike of some order β, 0 ≤ β < 1. Here µ is a suitable complex number so that the right hand side expression is analytic in $\mathbb{D}$ and the power is chosen to be the principal power. A similar problem for the class of convex functions of order β is open.     

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.     

Weighted norm inequalities for analytic functions

We present a weighted norm inequality involving convolutions of arbitrary analytic functions and certain confluent hypergeometric functions. This result implies a family of weighted norm inequalities both for entire functions of exponential type and for (generalized) hypergeometric series. The approach is based on author's general inequality for continuous functions and some hypergeometric transformations.     

Linear spaces and linear-invariant families of locally univalent analytic functions

Let X be the set of functions f analytic in the unit disk D with derivatives f(z)0 in D, that satisfy the growth restriction f(z)/f(z)=0((1–|z|)^–1 (zD). The set X is equipped with a normed linear space structure. The topological structure of X and its relationship with linear-invariant families of locally univalent functions is investigated.This research was supported by the U. S. Army Research Office-Durham, Grant DA-ARO-D-31-124-G1151.     

Some radius problems related to a certain subclass of analytic functions

For real parameters α and β such that 0≤α1β,we denote by S(α,β) the class of normalized analytic functions which satisfy the following two-sided inequality:αR(zf′(z)/f(z))β,z∈U,where U denotes the open unit disk.We find a sufficient condition for functions to be in the class S(α,β) and solve several radius problems related to other well-known function classes.     

Some relations between additive functions,II

Aequationes mathematicae -     

Integral operators preserving certain analytic functions

The purpose of the present paper is to investigate some integral preserving properties for certain analytic functions in the open unit disk. We also obtain the conditions for close-to-convex functions in a sector. Our results contain some interesting corollaries as the special cases.     

On certain classes of analytic functions

In this paper we introduce some new classes of analytic functions which generalise several known sequence spaces and function spaces studied by Simons, Maddox, Srivastava and others. We establish some inclusion relations, topological results and give the characterisation of continuous linear functionals for these spaces. Our results include the corresponding results of Simons, Maddox and others.     

Quasi-Hadamard product of a generalized class of analytic and univalent functions

In this paper, we introduce new subclasses of analytic and univalent functions and establish certain results concerning the quasi-Hadamard product of functions in these subclasses. Our result includes several previous known results as special cases.