Suppose that g(z)=z+a_2z^2+…is analytic for |z|<1, The condition Re{z g(z)/g(z)}>0 for |z|<1 (1) is necessary and sufficient for g(z) to be univalent and starlike for |z|<1. The condition Re{z g″(z)/g′(...Suppose that g(z)=z+a_2z^2+…is analytic for |z|<1, The condition Re{z g(z)/g(z)}>0 for |z|<1 (1) is necessary and sufficient for g(z) to be univalent and starlike for |z|<1. The condition Re{z g″(z)/g′(z)+1}>0 for |z|<1 (2) is necessary and sufficient for g(z) to be univalent and convex for |z|<1 In this paper we determine the radius Univalence (and starlikeness) of f(z) assodated with each of the cases (ⅰ) g(z) satisfies Re {g(z)/z}>0 for |z|<1 (ⅱ) g(z) satisfies eq .(1), (ⅲ) g(z) satisfies eq. (2). Definition. Let N_αdenote the class of functions f(z) which are regular in|z|<1 and are normalized by f(0)=1 and map |z|<1 into region D_α=展开更多
文摘Suppose that g(z)=z+a_2z^2+…is analytic for |z|<1, The condition Re{z g(z)/g(z)}>0 for |z|<1 (1) is necessary and sufficient for g(z) to be univalent and starlike for |z|<1. The condition Re{z g″(z)/g′(z)+1}>0 for |z|<1 (2) is necessary and sufficient for g(z) to be univalent and convex for |z|<1 In this paper we determine the radius Univalence (and starlikeness) of f(z) assodated with each of the cases (ⅰ) g(z) satisfies Re {g(z)/z}>0 for |z|<1 (ⅱ) g(z) satisfies eq .(1), (ⅲ) g(z) satisfies eq. (2). Definition. Let N_αdenote the class of functions f(z) which are regular in|z|<1 and are normalized by f(0)=1 and map |z|<1 into region D_α=
