The Fekete-Szegö problem for starlike mappings and nonlinear resolvents of the Carathéodory family on the unit balls of complex Banach spaces

In this paper, we first give a coefficient inequality for holomorphic functions on the unit disc U in C which are subordinate to a holomorphic function p on U with p ′ ( 0 ) ≠ 0 . Next, as applications of this theorem, we will give the Fekete-Szegö inequality for subclasses of normalized starlike ma...

Full description

Saved in:
Bibliographic Details
Published inAnalysis and mathematical physics Vol. 11; no. 3
Main Authors Hamada, Hidetaka, Kohr, Gabriela, Kohr, Mirela
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 2021
Springer Nature B.V
Subjects
Analysis
Analytic functions
Banach spaces
Inequality
Mathematical analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Carathéodory family
Subordination
30C45
Fekete-Szegö problem
Nonlinear resolvent
Starlike mapping
Quasi-convex mapping
32H02
Online AccessGet full text

Cover

More Information
Summary:In this paper, we first give a coefficient inequality for holomorphic functions on the unit disc U in C which are subordinate to a holomorphic function p on U with p ′ ( 0 ) ≠ 0 . Next, as applications of this theorem, we will give the Fekete-Szegö inequality for subclasses of normalized starlike mappings and normalized quasi-convex mappings of type B on the unit ball B of a complex Banach space. We also give the Fekete-Szegö inequality for ( 1 + r ) J r , where J r = J r [ f ] is the nonlinear resolvent of a mapping f in the Carathéodory family M ( B ) . Various particular cases will be also considered.
ISSN:1664-2368
1664-235X
DOI:10.1007/s13324-021-00557-6