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

Çetinkaya A., POLATOĞLU Y.

Hacettepe Journal of Mathematics and Statistics, cilt.47, sa.4, ss.813-820, 2018 (SCI-Expanded, Scopus, TRDizin) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 47 Sayı: 4
  • Basım Tarihi: 2018
  • Dergi Adı: Hacettepe Journal of Mathematics and Statistics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.813-820
  • İstanbul Kültür Üniversitesi Adresli: Hayır

Özet

We introduce a new class of harmonic function f, that is subclass of planar harmonic mapping associated with q− difference operator. Let h and g are analytic functions in the open unit disc D = {z : |z| < 1}. If f = h + g is the solution of the non-linear partial dierential equation wq(z) = Dqg(z) Dqh(z) = fz fz with |wq(z)| < 1, wq(z) ≺ b1 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 SHCq(b). Obviously that the class SHCq(b) is the subclass of SH. In this paper, we investigate properties of the class SHCq(b) by using subordination techniques.