Let f = h(z) + <(g(z))over bar> be a sense-preserving harmonic mapping in the open unit disc D = {z vertical bar vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar 1/b(1) g'(z)/h' (z) - M vertical ...

In this paper we investigate some properties of log-harmonic starlike mappings. For this aim we use the subordination principle or Lindelof Principle (Lewandowski (1961) [71).

Let f = h + (g) over bar be a harmonic function in the unit disc . We will give some properties of f under the condition the second dilatation is alpha-spiral.

Let CC(b) be the class of functions close-to-convex functions of order b, and let SH be the class of harmonic mappings in the plane. In the present paper we investigate harmonic mappings related to close-to-convex functions ...

The main purpose of the present paper is to give the extent idea which was introduced by Robinson(1947) [6]. One of the interesting application of this extent idea is an investigation of the class of harmonic mappings ...

In the present paper we will give some properties of the subclass of harmonic mappings which is related to m-fold starlike functions in the open unit disc D = {z parallel to z vertical bar < 1}. Throughout this paper we ...

The class of bounded radius of rotation is generalization of the convex functions. The concept of functions bounded boundary rotation originated from Loewner (1917). But he did not use the present terminology. It was Paatero ...

Let f = h(z) + g(z) be a univalent sense-preserving harmonic mapping of the open unit disc D = {z/vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar omega(z)vertical bar = vertical bar g'(z)/h'(z)vertical ...

A fundamental result of this paper shows that the transformation F=az(h(z+a/1+(a) over barz) + /(h(a) + <(g(a))over bar>(z + a) (1 + (a) over barz) defines a function in S0 HS* whenever f = h( z) + g( z) is S0 HS*, andwewill ...