q−q−q-Harmonic mappings for which analytic part is q−q−q-convex functions of complex order

Asena ÇETİNKAYA; Yaşar POLATOĞLU

Article Details

q−q−q-Harmonic mappings for which analytic part is q−q−q-convex functions of complex order

Authors:

Asena ÇETİNKAYA | Yaşar POLATOĞLU

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2018 Vol.47 Issue 4, pp.813-820

Document Type:

Article

Publication Date:

7/2018

Document Language:

English

Document ID (Org No.):

2000451856

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X

Abstract:

 

We introduce a new class of harmonic function fff, that is subclass of planar harmonic mapping associated with q−q−q-difference operator. Let hhh and ggg are analytic functions in the open unit disc D={z:|z|<1}D={z:|z|<1}\mathbb{D}=\{ z\,:\,|z|<1 \}. If f=h+¯gf=h+g¯f=h+\bar{g} is the solution of the non-linear partial differential equation wq(z)=Dqg(z)Dqh(z)=¯f¯zfzwq(z)=Dqg(z)Dqh(z)=f¯z¯fzw_q(z)=\dfrac{D_q g(z)}{D_q h(z)}=\dfrac{\bar{f}_\bar{z}}{f_z} with |wq(z)|<1|wq(z)|<1|w_q(z)|<1, wq(z)≺b11+z1−qzwq(z)≺b11+z1−qzw_q(z)\prec b_1 \dfrac{1+z}{1-qz} and hhh is q−q−q-convex function of complex order, then the class of such functions are called q−q−q-harmonic functions for which analytic part is q−q−q-convex functions of complex order denoted by SHCq(b)SHCq(b)\mathcal{S}_{ \mathcal{H}\mathcal{C}_q(b)}. Obviously that the class SHCq(b)SHCq(b)\mathcal{S}_{ \mathcal{H}\mathcal{C}_q(b)} is the subclass of SHSH\mathcal{S}_\mathcal{H}. In this paper, we investigate properties of the class SHCq(b)SHCq(b)\mathcal{S}_{ \mathcal{H}\mathcal{C}_q(b)} by using subordination techniques.

Article Details

q−q−q-Harmonic mappings for which analytic part is q−q−q-convex functions of complex order

Authors: Asena ÇETİNKAYA | Yaşar POLATOĞLU

Publisher: Hacettepe University

Main Topics: Mathematics

Journal: Hacettepe Journal of Mathematics and Statistics 2018 Vol.47 Issue 4, pp.813-820

Document Type: Article

Publication Date: 7/2018

Document Language: English

Document ID (Org No.): 2000451856

Frequency: Bimonthly

eISSN: 2651-477X

pISSN: 2651-477X

Issues

Authors:

Asena ÇETİNKAYA | Yaşar POLATOĞLU

Publisher:

Hacettepe University

Main Topics:

Mathematics

Journal:

Hacettepe Journal of Mathematics and Statistics 2018 Vol.47 Issue 4, pp.813-820

Document Type:

Article

Publication Date:

7/2018

Document Language:

English

Document ID (Org No.):

2000451856

Frequency:

Bimonthly

eISSN:

2651-477X

pISSN:

2651-477X