Subordination by Univalent  H  1  Functions | Zendy

AbuMuhanna Yusuf | Zendy; Hallenbeck D. J. | Zendy

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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 ).

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