A proof of a conjecture on convolution of harmonic mappings and some related problems

Yalçın Tokgöz S., Ebadian A., Azizi S.

Ukrainian Mathematical Journal, cilt.73, sa.2, ss.329-336, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 73 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s11253-021-01927-w
  • Dergi Adı: Ukrainian Mathematical Journal
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.329-336
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

Recently, Kumar, et al. proposed a conjecture concerning the convolution of a generalized right half-plane mapping with a vertical strip mapping. They verified this conjecture for n = 1, 2, 3 and 4. Moreover, it was proved only for ss =./2. By using of a new method, we settle this conjecture in the affirmative way for all n 2 N and ss 2 (0,.). Moreover, we apply this method to prove some results on the convolutions of harmonic mappings. The proposed new method simplifies calculations and remarkably shortens the proof of the results.