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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 ...

#### Some properties of starlike harmonic mappings

(Springer International Publishing AG, 2012)

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 ...

#### Some inequalities which hold for starlike log-harmonic mappings of order alpha

(Eudoxus Press, LLC., 2014-04)

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 ...

#### 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 ...

#### A certain class of harmonic mappings related to functions of bounded boundary rotation

(Eudoxus Press, 2014-05)

Let V(k) be the class of functions with bounded boundary rotation and let S-H be the class of sense-preserving harmonic mappings. In the present paper we investigate a certain class of harmonic mappings related to the ...

#### Some results on a starlike log-harmonic mapping of order alpha

(Elsevier Science BV, 2014-01-15)

Let H(D) be the linear space of all analytic functions defined on the open unit disc D = z is an element of C : vertical bar z vertical bar < 1. A sense preserving log-harmonic mapping is the solution of the non-linear ...

#### Subclass of m-quasiconformal harmonic functions in association with Janowski starlike functions

(Elsevier Science Inc, 2018-02-15)

Let's take f(z) = h (z) + <(g(z))over bar> which is an univalent sense-preserving harmonic functions in open unit disc D = {z : vertical bar z vertical bar < 1}. If f (z) fulfills vertical bar w(z)vertical bar = ...

#### 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 ...