Hitoshi Saitoh

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.

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).

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.

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 ).

Differential inequalities for certain analytic functions

The purpose of the present paper is to derive some differential inequalities for certain analytic functions in the open unit disk by appealing to a result obtained by the first author. Relevant connections of the results presented here with those obtained in earlier works are also pointed out.

On the rate of change of argdf(z) and argf(z)

Abstract The object of the present paper is to show the rate of change of argdf(z) and argf(z) for certain analytic functions in the unit disk.