Some classes of harmonic mappings with analytic part defined by subordination

Abstract

Let SHbe the class of functions f = h + g¯ that are harmonic univalent and sense-preserving in the open unit disk U = {z ∈ C : |z| < 1}, where h, g are analytic and f (0) = fz′ (0) − 1 = 0 in U. In this paper, we investigate the properties of some subclasses of SH such that h(z) is a starlike (or convex) function defined by subordination. We provide coefficient estimates, extremal function, distortion and growth estimates of g , growth, and Jacobian estimates of f . We also obtain area estimates and covering theorems of the classes. The results presented here generalize some known results.