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

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

Ukrainian Mathematical Journal, vol.73, no.2, pp.329-336, 2021 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 73 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.1007/s11253-021-01927-w
  • Journal Name: Ukrainian Mathematical Journal
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Page Numbers: pp.329-336
  • Bursa Uludag University Affiliated: Yes

Abstract

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.