ON A SUBCLASS OF CLOSE TO CONVEX FUNCTIONS

【摘要】 Let C ′(α,β) be the class of functions f(z)=(a~nz~n)from n=2 to ∞ 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))+(1-2a))<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.更多还原

【Abstract】 Let C ′(α,β) be the class of functions f(z)=(a~nz~n)from n=2 to ∞ 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))+(1-2a))<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.更多还原