Majorization Results Based upon the Bernardi Integral Operator

By making use of some families of integral and derivative operators, many distinct subclasses of analytic, starlike functions, and symmetric starlike functions have already been defined and investigated from numerous perspectives. In this article, with the help of the one-parameter Bernardi integral...

Full description

Saved in:
Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 7; p. 1404
Main Authors Al-Shbeil, Isra, Srivastava, Hari Mohan, Arif, Muhammad, Haq, Mirajul, Khan, Nazar, Khan, Bilal
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.07.2022
Subjects
analytic (holomorphic or regular) functions
Bernardi integral operator
carathéodory class of functions
Derivatives
Integrals
majorization problems
Mathematical analysis
Operators (mathematics)
Parameters
starlike functions
univalent functions
Online AccessGet full text

Cover

More Information
Summary:By making use of some families of integral and derivative operators, many distinct subclasses of analytic, starlike functions, and symmetric starlike functions have already been defined and investigated from numerous perspectives. In this article, with the help of the one-parameter Bernardi integral operator, we investigate several majorization results for the class of normalized starlike functions, which are associated with the Janowski functions. We also give some particular cases of our main results. Finally, we direct the interested readers to the possibility of examining the fundamental or quantum (or q-) extensions of the findings provided in this work in the concluding section. However, the (p,q)-variations of the suggested q-results will provide relatively minor and inconsequential developments because the additional (rather forced-in) parameter p is obviously redundant.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14071404