Abstract:
The object of the present paper is to consider the starlikeness and convexity of partial sums of certain analytic functions in the open unit disk.

Abstract:
A certain class B(n, ±, 2) of Bazilevi functions of order 2 in the unit disk is introduced. The object of the present paper is to derive some properties of functions belonging to the class B(n, ±, 2). Our result for the class B(n, ±, 2) is the improvement of the theorem by N. E. Cho ([1]).

Abstract:
The object ofthe present paper is to give some generalizations of results for certain analytic functions which were proved by Saitoh (Math. Japon. 35 (1990), 1073-1076). Our results contain some corollaries as the special cases.

Abstract:
We introduce the classes Kn* of analytic functions with negative coefficients by using the nth order Ruscheweyh derivative. The object of the present paper is to show coefficient inequalities and some closure theorems for functions f(z) in Kn*. Further we consider the modified Hadamard product of functions fi(z) in Kni*(n=1,2, ￠ € |,m).

Abstract:
Suffridge showed a result for subordinate functions. The object of the present paper is to show some subordinate theorems with the aid of the result by Suffridge.

Abstract:
A subclass 𝒞p(λ,μ)(p∈ℕ, 0<λ<1, −λ≦μ<1) of p-valently convex functions in the open unit disk 𝕌 is introduced. The object of the present paper is to discuss some interesting properties of functions belonging to the class 𝒞p(λ,μ).

Abstract:
For real α(α>1), we introduce subclasses M(α) and N(α) of analytic functions f(z) with f(0)=0 and f′(0)=1 in U. The object of the present paper is to consider the coefficient inequalities for functions f(z) to be in the classes M(α) and N(α). Further, the bounds of α for functions f(z) to be starlike in U are considered.