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#### 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 ...

#### 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 ...

#### 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 ...

#### Notes on Harmonic Functions for which the second Dilatation is α - spiral

(Eudoxus Press, 2015-06)

In this study, we consider, f = h + (g) over bar harmonic functions in the unit disc D. By applying S. S. Miller and P. M. Mocanu result, we obtain a new subclass of harmonic functions, such as S-HPST*(alpha, beta) We ...

#### An investigation of the certain class of multivalent harmonic mappings

(Eudoxus Press, 2016-03)

The main purpose of the present paper is to investigate some properties of the certain class of sense-preserving p-valent harmonic mappings in the open unit disc D = {z is an element of C parallel to z vertical bar < 1}.

#### 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 ...

#### Harmonic mappings related to starlike function of complex order α

(Işık University Press, 2014)

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 ...