We consider a class T O H of typically real harmonic functions on the unit disk that contains the class of normalized analytic and typically real functions. We also obtain some partial results about the region of univalence for this class.

We prove the existence of xed points of p-tupling renormalization operators for interval and circle mappings having a critical point of arbitrary real degree r > 1. Some properties of the resulting maps are studied: analyticity, univalence, behavior as r tends to innnity.

"In this paper, we consider the complex form of a new generalization Bernstein-Schurer operators. We obtain some quantitative upper estimates for approximation these operators attached to analytic functions. Moreover, prove that preserve properties original function such as univalence, starlikeness, convexity and spirallikeness."