SOME REMARKS FOR λ-SPIRALLIKE FUNCTION OF COMPLEX ORDER AT THE BOUNDARY OF THE UNIT DISC


Akyel T.

Communications of the Korean Mathematical Society, cilt.36, sa.4, ss.743-757, 2021 (ESCI, Scopus)

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 36 Sayı: 4
  • Basım Tarihi: 2021
  • Doi Numarası: 10.4134/ckms.c200336
  • Dergi Adı: Communications of the Korean Mathematical Society
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, zbMATH
  • Sayfa Sayıları: ss.743-757
  • Anahtar Kelimeler: Angular derivative, Holomorphic function, Schwarz lemma, Λ-spirallike function
  • Maltepe Üniversitesi Adresli: Evet

Özet

We consider a different version of Schwarz Lemma for λ-spirallike function of complex order at the boundary of the unit disc D: We estimate the modulus of the angular derivative of the function (Formula Presented) from below for λ-spirallike function f(z) of complex order at the boundary of the unit disc D by taking into account the zeros of the function f(z)-z which are different from zero. We also estimate the same function with the second derivatives of the function f at the points z = 0 and z = z0 ≠ 0 We show the sharpness of these estimates and present examples.