On a subclass of close to convex functions

Let C′  (α,β) be the class of functions f(z)=z+∑n=2∞anzn analytic in D = {z:|z|<1}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)-1zf'(z)g(z)+(1-2α)|<βfor 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.