Toshio Hayami

Some properties of certain analytic functions.

Let 𝒜p be the class of certain analytic functions f(z) in the open unit disk U. For f(z)∈𝒜p, a subclass 𝒜p(α,β,γ,j) of 𝒜p is introduced. The object of the present paper is to discuss some properties of functions f(z) belonging to class Ap(α,β,γ;j).

Differential subordination and argumental property

For analytic functions f(z) in the open unit disk E and convex functions g(z) in E, Ch. Pommerenke [Ch. Pommerenke, On close-to-convex analytic functions, Trans. Amer. Math. Soc. 114 (1) (1965) 176-186] has proved one theorem which is a generalization of the result by K. Sakaguchi [K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959) 72-75]. The object of the present paper is to generalize the theorem due to Pommerenke.

The Fekete-Szegö Problem for -Valently Janowski Starlike and Convex Functions

For -valently Janowski starlike and convex functions defined by applying subordination for the generalized Janowski function, the sharp upper bounds of a functional related to the Fekete-Szego problem are given.

A sufficient condition for p-valently harmonic functions

For normalized harmonic functions in the open unit disk , a sufficient condition on for to be -valent in is discussed. Moreover, some interesting examples and images of satisfying the obtained condition are enumerated.