On a subclass of close-to-convex functions with negative coefficients

Abstract EN

Let S*(a,(3) denote the class of functions /(z) = z- ^akzk{ak > 0) which are analytic in the unit disc U = {z : \z\ < l} and which satisfy the inequality 2z/'(z) f(.z)-f(-z) 2zf'(z) fU)-f(-z) + (l-2a)

Further /(z) is said to belong to the class C5(a, (3)(0 < a < 1 and 0 < (3 < 1) if and only if zf'iz) e S*s(a, (3).

The object of the present paper is to obtain distortion theorems, coefficient estimates, closure theorems for functions in the classes S*(a, (3) and Cs(a, (3).

Properties of the integral operator c+ I J tc~lf(t)dt, c > -1 are also studied.

Finally, we present a result about a fractional integral operator.