A new general idea for starlike and convex functions

Abstract

Let $\mathcal{A}$ be the class of functions $f(z)$ which are analytic in the open unit disk $\mathbb{U}$ with $f(0)=0$ and $f'(0)=1$. For the class $\mathcal{A}$, a new general class $\mathcal{A}_{k}$ is defined. With this general class $\mathcal{A}_{k}$, two interesting classes $\mathcal{S}_{k}^{\ast}(\alpha)$ and $\mathcal{K}_{k}(\alpha)$ concerning classes of starlike of order $\alpha$ in $\mathbb{U}$ and convex of order $\alpha$ in $\mathbb{U}$ are considered.

On Some Interesting Classes of Analytic Functions Related to Univalent Functions

“…The function f (z) given by (1) was considered by Owa [1] and Owa et al [2]. In [1], he considered the coefficient inequalities for the function f (z) and in [2], the authors considered the coefficient inequalities for functions in general subclasses.…”

“…The function f (z) given by (1) was considered by Owa [1] and Owa et al [2]. In [1], he considered the coefficient inequalities for the function f (z) and in [2], the authors considered the coefficient inequalities for functions in general subclasses. In the present paper, we consider some interesting properties of f (z) ∈ A concerning S * (α), C(α) and R(α) applying subordinations of f (z).…”

The Order of Strongly Starlikeness of the Generalized α-Convex Functions

“…The strongly-starlike functions and related functions have been extensively studied by several authors (see, e.g., [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]).…”