Hitoshi Shiraishi

Sufficient conditions for strongly Carathéodory functions

Recently, by applying the principle of subordination for analytic functions in the open unit disk U, Kim and Cho [I. H. Kim, N. E. Cho, Sufficient conditions for Caratheodory functions, Comput. Math. Appl. 59 (2010), 2067-2073] considered several sufficient conditions for a family of Caratheodory functions. The main purpose of this paper is to investigate some (presumably new) sufficient conditions for the class of strongly Caratheodory functions in U. One illustrative example and several corollaries of the main results presented here are also considered.

Reciprocal classes of p-valently spirallike and p-valently Robertson functions

AbstractFor p-valently spirallike and p-valently Robertson functions in the open unit disk U, reciprocal classes Sp(α,β), and Cp(α,β) are introduced. The object of the present paper is to discuss some interesting properties for functions f(z) belonging to the classes Sp(α,β) and Cp(α,β). 2010 Mathematics Subject Classification Primary 30C45

Sufficient conditions for starlikeness of order α for meromorphic functions

Let Σ be the class of functions F(z) which are meromorphic in the punctured open unit disk U∗. Applying the results by Nunokawa [M. Nunokawa, On properties of non-Caratheodory functions, Proc. Japan Acad. 68 (1992) 152–153] and Fukui and Sakaguchi [S. Fukui and K. Sakaguchi, An extension of a theorem of S. Ruscheweyh, Bull. Fac. Edu. Wakayama Univ. Nat. Sci. 29 (1980) 1–3], we derive some sufficient conditions for meromorphic strongly starlikeness for function F(z)∈Σ with some interesting corollaries.