TY - JOUR
T1 - Schwarzian derivative for convex mappings of order α
AU - Carrasco, Pablo
AU - Hernández, Rodrigo
N1 - Funding Information:
Pablo Carrasco and Rodrigo Hernández were partially supported by Fondecyt Grants # 1190756.
Funding Information:
We thank our colleague, prof. Iason Efraimidis, from Universidad Autónoma de Madrid, for his precise contribution to improve the presentation of the manuscript, and the proof of Theorem 6.
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Nature Switzerland AG.
PY - 2023/4
Y1 - 2023/4
N2 - The main purpose of this paper is to obtain sharp bounds of the norm of Schwarzian derivative for convex mappings of order alpha in terms of the value of f′ ′(0 ) , in particular, when this quantity is equal to zero. In addition, we obtain sharp bounds for distortion and growth for this mappings and we generalize the results obtained by Suita (J Hokkaido Univ Ed Sect II A 46(2):113–117, 1996) and Yamashita (Hokkaido Math J 28:217–230, 1999) for this particular case.
AB - The main purpose of this paper is to obtain sharp bounds of the norm of Schwarzian derivative for convex mappings of order alpha in terms of the value of f′ ′(0 ) , in particular, when this quantity is equal to zero. In addition, we obtain sharp bounds for distortion and growth for this mappings and we generalize the results obtained by Suita (J Hokkaido Univ Ed Sect II A 46(2):113–117, 1996) and Yamashita (Hokkaido Math J 28:217–230, 1999) for this particular case.
KW - Convex of order alpha
KW - Schwarz Lemma
KW - Schwarzian derivative
UR - http://www.scopus.com/inward/record.url?scp=85147533426&partnerID=8YFLogxK
U2 - 10.1007/s13324-023-00785-y
DO - 10.1007/s13324-023-00785-y
M3 - Article
AN - SCOPUS:85147533426
SN - 1664-2368
VL - 13
JO - Analysis and Mathematical Physics
JF - Analysis and Mathematical Physics
IS - 2
M1 - 22
ER -