Abstract:

The sharp pre-schwarzian norm of nonlinear transformation Jc［f］=∫z0(f′(ξ))cdξ is given, where f is a close-to-convex function and c is an arbitrary constant. By using of Becker’s univalence criteria, the condition on which Jc［f ]-maps a close-to-convex function to a univalent function is also obtained.

Key words: close-to-convex functions, non-linear transformations, univalency, pre-Schwarzain norm