Geometric properties and sections for certain subclasses of harmonic mappings

Let G(H)(k)(alpha; r) denote the subclasses of normalized harmonic mappings f = h+g in the unit disk D satisfying the condition Re in where and alpha >= 0. In this paper, we first provide the sharp coefficient estimates and the sharp growth theorems for harmonic mappings in the class G(H)(k)(alpha; 1). Next, we derive the geometric properties of harmonic mappings in G(H)(1)(alpha; 1). Then we study several properties of the sections of f is an element of G(H)k(alpha; 1). Finally, we show that if f is an element of P-H(0) (alpha) and F is an element of G(H)(1)(beta; 1), then the harmonic convolution f * F is univalent and close-to-convex harmonic function in the unit disk for alpha is an element of (1/2, 1), beta > 0.