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#### Quasiconformal harmonic mappings related to starlike functions

(Eudoxus Press, 2014-07)

Let f = h(z) + <(g(z))over bar> be a univalent sense-preserving harmonic mapping of the unit disc D = {z is an element of C parallel to z vertical bar < 1}. If f satisfies the condition vertical bar w(z)vertical bar = ...

#### Harmonic mappings related to Janowski starlike functions

(Elsevier Science BV, 2014-11)

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 ...

#### On the class of harmonic mappings which is related to the class of bounded boundary rotation

(Elsevier Science Inc, 2015-09-15)

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 ...

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

(Springer International Publishing, 2015-01-16)

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, ...

#### Harmonic mappings related to the m-fold starlike functions

(Elsevier Science Inc, 2015-09-15)

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 ...

#### Harmonic mappings related to Janowski convex functions of complex order b

(2013)

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 ...

#### Close-to-convex functions defined by fractional operator

(2013)

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. ...

#### Harmonic function for which the second dilatation is α-spiral

(Springer International Publishing AG, 2012)

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.