Certain class of harmonic mappings related to starlike functions

Let S∗ be the class of starlike functions and let SH be the class of harmonic mappings in the plane. In this paper we investigate harmonic mapping related to the starlike functions.Publisher's Versio

Quasiconformal harmonic mappings related to janowski starlike functions

Let be a univalent sense-preserving harmonic mapping of the open unit disc D = {z⎜ ⎜z⎜ < 1}. If f satisfies the condition ⎜ω(z)⎜= < k, 0 < k < 1, then is called k-quasiconformal harmonic mapping in D. The main purpose of this paper was to give some properties of the class of k-quasiconformal mappings related to Janowski starlike functions

Close-to-convex functions defined by fractional operator

Let S denote the class of functions f(z) = z + a2z2+... analytic and univalent in the open unit disc D = {z ∈ C||z| 0 in , and prove that every close-to-convex function is univalent. The normalized class of close-to-convex functions denoted by K. These classesare related by the proper inclusions C ⊂ S* ⊂ K ⊂ S. In this paper, we generalize the close-to-convex functions and denote K(λ) the class of such functions. Various properties of this class of functions is alos studied.Publisher's Versio

Harmonic mappings for which co-analytic part is a close-to-convex function of order b

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, 2003).Publisher's Versio

Harmonic mappings related to Janowski convex functions of complex order b

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 generalized of R. J. Libera Theorem [7].Publisher's Versio

Harmonic function for which the second dilatation is α-spiral

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.Publisher's Versio

Harmonic mappings related to Janowski starlike 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 related to Janowski starlike functions.Publisher's Versio