A Note on Sufficient Conditions for Sakaguchi Type Functions of Order \(\beta\)

Abstract

In this paper we obtain some sufficient conditions for Sakaguchi type functions of order \(\beta\), \(S_{n}(\beta,s,t)\) defined as the class of normalized analytic functions in the open unit disc satisfying \(\Re\left\{\frac{(s-t)zf'(z)}{f(sz)-f(tz)}\right\}>\beta\), \(s\), \(t\in \mathbb{R}\),  \(s\neq t\), and \(0\leq\beta<1\).