ON BOUNDS FOR THE DERIVATIVE OF ANALYTIC FUNCTIONS AT THE BOUNDARY
Korean Journal of Mathematics, cilt.29, sa.4, ss.785-800, 2021 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 29 Sayı: 4
- Basım Tarihi: 2021
- Doi Numarası: 10.11568/kjm.2021.29.4.785
- Dergi Adı: Korean Journal of Mathematics
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
- Sayfa Sayıları: ss.785-800
- Anahtar Kelimeler: Analytic function, Angular derivative, Julia-Wolff lemma, Schwarz lemma
- Maltepe Üniversitesi Adresli: Evet
Özet
In this paper, we obtain a new boundary version of the Schwarz lemma for analytic function. We give sharp upper bounds for |f′ (0)| and sharp lower bounds for |f′ (c)| with c ∈ ∂D = {z: |z| = 1}. Thus we present some new inequalities for analytic functions. Also, we estimate the modulus of the angular derivative of the function f(z) from below according to the second Taylor coefficients of f about z = 0 and z = z0 ≠ 0. Thanks to these inequalities, we see the relation between |f′ (0)| and ℜf(0). Similarly, we see the relation between ℜf(0) and |f′ (c)| for some c ∈ ∂D. The sharpness of these inequalities is also proved.