Yıl 2018, Cilt 47, Sayı 4, Sayfalar 813 - 820 2018-08-01
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## $q-$Harmonic mappings for which analytic part is $q-$convex functions of complex order

#### Asena Çetinkaya [1] , Yaşar Polatoğlu [2]

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We introduce a new class of harmonic function $f$, that is subclass of planar harmonic mapping associated with $q-$difference operator. Let $h$ and $g$ are analytic functions in the open unit disc $\mathbb{D}=\{ z\,:\,|z|<1 \}$. If $f=h+\bar{g}$ is the solution of the non-linear partial differential equation $w_q(z)=\dfrac{D_q g(z)}{D_q h(z)}=\dfrac{\bar{f}_\bar{z}}{f_z}$ with $|w_q(z)|<1$, $w_q(z)\prec b_1 \dfrac{1+z}{1-qz}$ and $h$ is $q-$convex function of complex order, then the class of such functions are called $q-$harmonic functions for which analytic part is $q-$convex functions of complex order denoted by $\mathcal{S}_{ \mathcal{H}\mathcal{C}_q(b)}$. Obviously that the class $\mathcal{S}_{ \mathcal{H}\mathcal{C}_q(b)}$ is the subclass of $\mathcal{S}_\mathcal{H}$. In this paper, we investigate properties of the class $\mathcal{S}_{ \mathcal{H}\mathcal{C}_q(b)}$ by using subordination techniques.
$q-$difference operator, $q-$harmonic mapping, $q-$convex function of complex order
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Birincil Dil en Matematik Matematik Yazar: Asena Çetinkaya (Sorumlu Yazar) Yazar: Yaşar Polatoğlu
 Bibtex @araştırma makalesi { hujms452853, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {1303-5010}, address = {Hacettepe Üniversitesi}, year = {2018}, volume = {47}, pages = {813 - 820}, doi = {}, title = {\$q-\$Harmonic mappings for which analytic part is \$q-\$convex functions of complex order}, key = {cite}, author = {Polatoğlu, Yaşar and Çetinkaya, Asena} } APA Çetinkaya, A , Polatoğlu, Y . (2018). $q-$Harmonic mappings for which analytic part is $q-$convex functions of complex order. Hacettepe Journal of Mathematics and Statistics, 47 (4), 813-820. Retrieved from http://dergipark.gov.tr/hujms/issue/38872/452853 MLA Çetinkaya, A , Polatoğlu, Y . "$q-$Harmonic mappings for which analytic part is $q-$convex functions of complex order". Hacettepe Journal of Mathematics and Statistics 47 (2018): 813-820 Chicago Çetinkaya, A , Polatoğlu, Y . "$q-$Harmonic mappings for which analytic part is $q-$convex functions of complex order". Hacettepe Journal of Mathematics and Statistics 47 (2018): 813-820 RIS TY - JOUR T1 - $q-$Harmonic mappings for which analytic part is $q-$convex functions of complex order AU - Asena Çetinkaya , Yaşar Polatoğlu Y1 - 2018 PY - 2018 N1 - DO - T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 813 EP - 820 VL - 47 IS - 4 SN - 1303-5010- M3 - UR - Y2 - 2017 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics $q-$Harmonic mappings for which analytic part is $q-$convex functions of complex order %A Asena Çetinkaya , Yaşar Polatoğlu %T $q-$Harmonic mappings for which analytic part is $q-$convex functions of complex order %D 2018 %J Hacettepe Journal of Mathematics and Statistics %P 1303-5010- %V 47 %N 4 %R %U ISNAD Çetinkaya, Asena , Polatoğlu, Yaşar . "$q-$Harmonic mappings for which analytic part is $q-$convex functions of complex order". Hacettepe Journal of Mathematics and Statistics 47 / 4 (Ağustos 2018): 813-820.