Mamoru Nunokawa

Close-to-convexity, starlikeness, and convexity of certain analytic functions☆

The main object of the present paper is to derive several sufficient conditions for close-to-convexity, starlikeness, and convexity of certain (normalized) analytic functions. Relevant connections of some of the results obtained in this paper with those in earlier works are also provided.

A certain connection between starlike and convex functions

Abstract We define two certain classes of functions S ∗ (α, β) and C(α, β) and obtain a certain connection between these classes.

A certain class of multivalent functions

Abstract The object of the present paper is to derive several properties of a certain class of multivalent functions in the open unit disk. One of our main theorems unifies and extends several earlier results in the theory of analytic functions.

On Certain Multivalent Functions

Let a#x1D4AE;*(p,α) be the class of functions f(z) which are analytic and p-valently starlike of order α in the open unit disk E. The object of the present paper is to derive an interesting condition for f(z) to be in the class a#x1D4AE;*(p,α).

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.

On some sufficient conditions for univalence and starlikeness

In this work, the conditions for univalence, starlikeness and convexity are discussed.MSC:30C45, 30C80.

AN APPLICATION OF A CERTAIN INTEGRAL OPERATOR

Abstract The object of the present paper is to show an application of a certain integral operator for analytic functions in the unit disk.

On starlikeness of libera transformation

Recently, Mocana [6] has proved that if is analytic in in , then F(z) is starlike in where . In this paper, we will improve the above result.

Some properties of analytic functions relating to the Miller and Mocanu result

Let P(@a) be the class of analytic functions p(z) in the open unit disc U with p(0)=1 and |argp(z)| 0. The object of the present paper is to discuss some properties of p(z) in the class P(@a). Furthermore, an example for our results is shown.

Neighborhoods of certain analytic functions

Abstract Two subclasses P n (α) and Q n (α) of certain analytic functions in the open unit disk U are introduced. For p ( z ) ∈ P n ( α ) and δ n ⩾ 0, the δ n -neighborhood N δ n ( p ( z )) of p ( z ) is defined. For P n ( α ), Q n ( α ), and N δn ( p ( z )), we prove that if p ( z ) ∈ Q n ( α ), then N ( 1− α ) δ > n ( p ( z )) ⊂ P n ( α ).