Majorization results based upon the Bernardi integral operator
Date
2022
Authors
Al-Shbeil, Isra
Srivastava, H.M.
Arif, Muhammad
Haq, Mirajul
Khan, Nazar
Khan, Bilal
Journal Title
Journal ISSN
Volume Title
Publisher
Symmetry
Abstract
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
Description
Keywords
analytic (holomorphic or regular) functions, univalent functions, starlike functions, majorization problems, Bernardi integral operator, carathéodory class of functions
Citation
Al-Shbeil, I., Srivastava, H., Arif, M., Haq, M., Khan, N., & Khan, B. (2022). “Majorization results based upon the Bernardi integral operator.” Symmetry, 14(7), 1404. https://doi.org/10.3390/sym14071404