An application of a subordination chain

Let K denote the class of functions g(z)=z+a2z2+⋯ which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f(0)=0, then for g∈K, f(z)+αzf′(z) ≺ g(z)+αzg′(z) in E implies that f(z)≺g(z) in E, where α>0 is a real number and the symbol ≺ s...

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Main Authors: Sukhjit Singh, Sushma Gupta
Format: Article
Language:English
Published: Wiley 2003-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171203204087
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author Sukhjit Singh
Sushma Gupta
author_facet Sukhjit Singh
Sushma Gupta
author_sort Sukhjit Singh
collection DOAJ
description Let K denote the class of functions g(z)=z+a2z2+⋯ which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f(0)=0, then for g∈K, f(z)+αzf′(z) ≺ g(z)+αzg′(z) in E implies that f(z)≺g(z) in E, where α>0 is a real number and the symbol ≺ stands for subordination.
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spelling doaj-art-a6959d0d8ed94e0e878f6ceac53dc5702025-08-20T03:38:39ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003271751175410.1155/S0161171203204087An application of a subordination chainSukhjit Singh0Sushma Gupta1Department of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148, Punjab 106, IndiaDepartment of Mathematics, Sant Longowal Institute of Engineering and Technology, Longowal-148, Punjab 106, IndiaLet K denote the class of functions g(z)=z+a2z2+⋯ which are regular and univalently convex in the unit disc E. In the present note, we prove that if f is regular in E, f(0)=0, then for g∈K, f(z)+αzf′(z) ≺ g(z)+αzg′(z) in E implies that f(z)≺g(z) in E, where α>0 is a real number and the symbol ≺ stands for subordination.http://dx.doi.org/10.1155/S0161171203204087
spellingShingle Sukhjit Singh
Sushma Gupta
An application of a subordination chain
International Journal of Mathematics and Mathematical Sciences
title An application of a subordination chain
title_full An application of a subordination chain
title_fullStr An application of a subordination chain
title_full_unstemmed An application of a subordination chain
title_short An application of a subordination chain
title_sort application of a subordination chain
url http://dx.doi.org/10.1155/S0161171203204087
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