Premium
Subordination by Univalent H 1 Functions
Author(s) -
AbuMuhanna Yusuf,
Hallenbeck D. J.
Publication year - 1987
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/blms/19.3.249
Subject(s) - mathematics , subordination (linguistics) , univalent function , element (criminal law) , combinatorics , class (philosophy) , convex hull , order (exchange) , unit (ring theory) , hull , set (abstract data type) , regular polygon , pure mathematics , geometry , analytic function , philosophy , linguistics , mathematics education , finance , artificial intelligence , marine engineering , political science , computer science , law , economics , programming language , engineering
Suppose that F is an element of H 1 (Hardy class of order 1 over the unit disc) and F is a univalent starlike mapping. Let s ( F ) denote the set of functions subordinate to F and Hs ( F ) the closed convex hull of s ( F ). We prove that f ∈ Hs ( F ) and ‖ f ‖ 1 = ‖ F ‖ 1 then f is an element of s ( F ).