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 ...

Let H(D) be the linear space of all analytic functions defined on the open disc D = {z vertical bar vertical bar z vertical bar < 1}. A log-harmonic mappings is a solution of the nonlinear elliptic partial differential ...

In the present paper we investigate a class of harmonic mappings for which the second dilatation is a close-to-convex function of complex order b, b is an element of C/{0} (Lashin in Indian J. Pure Appl. Math. 34(7):1101-1108, ...

For log-harmonic functions f(z) = zh(z)g(z) in the open unit disk U, two subclasses H*LH(?) and G*LH(?) of S*LH(?) consisting of all starlike log-harmonic functions of order ? (0 ? ? &lt; 1) are considered. The object of ...

Let SH be the class of all sense-preserving harmonic mappings in the open unit disc D = {z ∈ ℂ||z| < 1}. In the present paper the authors investigate the properties of the class of harmonic mappings which is based on the ...

Let S denote the class of functions f(z) = z + a2z2+... analytic and univalent in the open unit disc D = {z ∈ C||z|<1}. Consider the subclass and S* of S, which are the classes ofconvex and starlike functions, respectively. ...

Let SH be the class of harmonic mappings defined by SH = { f = h(z) + g(z) | h(z) = z + ∑∞ n=2 anzⁿ, g(z) = ∑∞ n=1 bnzⁿ} The purpose of this talk is to present some results about harmonic mappings which was introduced by ...

Let SH be the class of harmonic mappings defined by SH = { f = h(z) + g(z)| h(z) = z + ∑∞ n=2 anzⁿ, g(z) = b1z + ∑∞ n=2 bnzⁿ, b1 < 1 } where h(z) and g(z) are analytic. Additionally f(z) ∈ SH(α) ⇔ | zh′ (z) − zg′(z) h(z) ...

Let f(z) be an analytic function in the open unit disk D normalized with f(0) = 0 and f'(0) = 1. With the help of subordinations, for convex functions f(z) in D, the order of close-to-convexity for f(z) is discussed with ...

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.