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#### Quasiconformal Harmonic Mappings Related to Janowski Starlike Functions

(Univ Kebangsaan Malaysia, Faculty Science & Technology, Bangi, Selangor, 43600, Malaysia, 2014-12)

Let f(z) = h(z) + <(g(z))over bar> be a univalent sense-preserving harmonic mapping of the open unit disc D = {z vertical bar vertical bar z vertical bar < 1}. If f satisfies the condition vertical bar omega(z)vertical ...

#### q-Starlike Functions of Order Alpha

(Turkic World Mathematical Soc, Z Khalilov Str, 23, Baku, Az 1148, Azerbaijan, 2018)

For all q is an element of (0, 1) and 0 <= alpha < 1 we define a class of analytic functions, so-called q-starlike functions of order alpha on the open unit disc D = {z : vertical bar z vertical bar < 1}. We will study ...

#### Some properties of starlike harmonic mappings

(Springer International Publishing Ag, Gewerbestrasse 11, Cham, Ch-6330, Switzerland, 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*, ...

#### Harmonic mappings for which second dilatation is Janowski functions

(2013)

In the present paper we extend the fundamental property that if
h(z) and g(z) are regular functions in the open unit disc D with the
properties h(0) = g(0) = 0, h maps D onto many-sheeted region which
is starlike with ...

#### Some properties of q- close-to-convex functions

(Hacettepe Univ, Fac Sci, Hacettepe Univ, Fac Sci, Beytepe, Ankara 06800, Turkey, 2017-12)

Quantum calculus had been used first time by M.E.H.Ismail, E.Merkes and D.Steyr in the theory of univalent functions [5].
In this present paper we examine the subclass of univalent functions which is defined by quantum ...

#### Some distortion theorems for starlike harmonic functions

(2010)

In this paper , we consider harmonic univalent mappings of the form f = h + ¯g defined on the unit disk D which are starlike. Distortion and growth theorems are obtained.

#### Application Of The Subordination Principle To The Multivalent Harmonic Mappings With Shear Construction Method

(Pergamon-Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, Oxford Ox5 1Gb, England, 2011-06)

The harmonic function in the open unit disc D = (z is an element of C vertical bar z vertical bar < 1} can be written as a sum of an analytic and an anti-analytic function. f = h(z) + g(z), where h(z) and g(z) are analytic ...

#### Harmonic Function For Which The Second Dilatation is Alpha-Spiral

(Springer International Publishing Ag, Gewerbestrasse 11, Cham, Ch-6330, Switzerland, 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

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

(2015)

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 ∈ C/{0} (Lashin
in Indian J. Pure Appl. Math. 34(7):1101-1108, 2003).

#### Some properties of q- close-to-convex functions

(2017)

Quantum calculus had been used first time by M.E.H.Ismail, E.Merkes
and D.Steyr in the theory of univalent functions [5].
In this present paper we examine the subclass of univalent functions
which is defined by quantum ...