Majorization Results for Certain Subfamilies of Analytic Functions

Majorization Results for Certain Subfamilies of Analytic Functions

Let h1z and h2z be two nonvanishing holomorphic functions in the open unit disc with h10=h20=1. For some holomorphic function qz, we consider the class consisting of normalized holomorphic functions f whose ratios fz/zqz and qz are subordinate to h1z and h2z, respectively. The majorization results a...

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Main Authors: Muhammad Arif, Miraj Ul-Haq, Omar Barukab, Sher Afzal Khan, Saleem Abullah
Format: Article
Language:English
Published: Hindawi Limited 2021-01-01
Series:Journal of Function Spaces
Online Access:http://dx.doi.org/10.1155/2021/5548785
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spelling doaj-22f668be516e45c7b316f6a5538a580b2021-04-19T00:05:06ZengHindawi LimitedJournal of Function Spaces2314-88882021-01-01202110.1155/2021/5548785Majorization Results for Certain Subfamilies of Analytic FunctionsMuhammad Arif0Miraj Ul-Haq1Omar Barukab2Sher Afzal Khan3Saleem Abullah4Faculty of Physical and Numerical SciencesFaculty of Physical and Numerical SciencesFaculty of Computing and Information TechnologyFaculty of Physical and Numerical SciencesFaculty of Physical and Numerical SciencesLet h1z and h2z be two nonvanishing holomorphic functions in the open unit disc with h10=h20=1. For some holomorphic function qz, we consider the class consisting of normalized holomorphic functions f whose ratios fz/zqz and qz are subordinate to h1z and h2z, respectively. The majorization results are obtained for this class when h1z is chosen either h1z=cosz or h1z=1+sinz or h1z=1+z and h2z=1+sinz.http://dx.doi.org/10.1155/2021/5548785
collection DOAJ
language English
format Article
sources DOAJ
author Muhammad Arif
Miraj Ul-Haq
Omar Barukab
Sher Afzal Khan
Saleem Abullah
spellingShingle Muhammad Arif
Miraj Ul-Haq
Omar Barukab
Sher Afzal Khan
Saleem Abullah
Majorization Results for Certain Subfamilies of Analytic Functions
Journal of Function Spaces
author_facet Muhammad Arif
Miraj Ul-Haq
Omar Barukab
Sher Afzal Khan
Saleem Abullah
author_sort Muhammad Arif
title Majorization Results for Certain Subfamilies of Analytic Functions
title_short Majorization Results for Certain Subfamilies of Analytic Functions
title_full Majorization Results for Certain Subfamilies of Analytic Functions
title_fullStr Majorization Results for Certain Subfamilies of Analytic Functions
title_full_unstemmed Majorization Results for Certain Subfamilies of Analytic Functions
title_sort majorization results for certain subfamilies of analytic functions
publisher Hindawi Limited
series Journal of Function Spaces
issn 2314-8888
publishDate 2021-01-01
description Let h1z and h2z be two nonvanishing holomorphic functions in the open unit disc with h10=h20=1. For some holomorphic function qz, we consider the class consisting of normalized holomorphic functions f whose ratios fz/zqz and qz are subordinate to h1z and h2z, respectively. The majorization results are obtained for this class when h1z is chosen either h1z=cosz or h1z=1+sinz or h1z=1+z and h2z=1+sinz.
url http://dx.doi.org/10.1155/2021/5548785
work_keys_str_mv AT muhammadarif majorizationresultsforcertainsubfamiliesofanalyticfunctions
AT mirajulhaq majorizationresultsforcertainsubfamiliesofanalyticfunctions
AT omarbarukab majorizationresultsforcertainsubfamiliesofanalyticfunctions
AT sherafzalkhan majorizationresultsforcertainsubfamiliesofanalyticfunctions
AT saleemabullah majorizationresultsforcertainsubfamiliesofanalyticfunctions
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