关键词: starlike, convex, close to convex, radius of convexity

Abstract:

Let C'(α，β) be the class of functions f(z)=z+Σ^∞_n=2a_nz_n analytic in D={z: |z|<1}, satisfying for some convex function g(z) with g(0)=g'(0)-1=0 and for all z in D the condition

|{zf'(z)/{g(z) -1/zf'(z)/{g(z)}+(1-2α)|<β

for some α，β(0≤α<1, 0<β≤1). A sharp coefficient estimate, distortion theorems and radius of convexity are determined for the class C'(α, β). The results extend the work of C. Selvaraj.

Key words: starlike, convex, close to convex, radius of convexity