Convolutions of planar harmonic strip mappings

Dorff M., Hamidi S. G., Jahangiri J. M., Yaar E.

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, cilt.66, sa.11, ss.1904-1921, 2021 (SCI-Expanded, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 66 Sayı: 11
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1080/17476933.2020.1789864
  • Dergi Adı: COMPLEX VARIABLES AND ELLIPTIC EQUATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.1904-1921
  • Anahtar Kelimeler: Convolutions, planar harmonic mappings, directional convexity
  • Bursa Uludağ Üniversitesi Adresli: Evet

Özet

We consider classes of harmonic univalent functions f(k) = h(k) + (g) over bar (k), (k = 1, 2) that are shears of the analytic map h(k) - g(k) = 1/2 log[(1 + z) / (1 - z)] with dilatation omega(k) = e(i theta k) z(k). We prove that if the convolution f(1) * f(2) is locally one-to-one and sense-preserving, then f(1) * f(2) is convex in the direction of the real axis.