Inclusion Properties of p -Valent Functions Associated with Borel Distribution Functions

Ebrahim Amini, Mojtaba Fardi, Mahmoud A. Zaky, António M. Lopes () and Ahmed S. Hendy
Additional contact information
Ebrahim Amini: Department of Mathematics, Payme Noor University, Tehran P.O. Box 19395-4697, Iran
Mojtaba Fardi: Department of Applied Mathematics, Faculty of Mathematical Sciences, Shahrekord University, Shahrekord P.O. Box 115, Iran
Mahmoud A. Zaky: Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh 13314, Saudi Arabia
António M. Lopes: LAETA/INEGI, Faculty of Engineering, University of Porto, 4200-465 Porto, Portugal
Ahmed S. Hendy: Department of Computational Mathematics and Computer Science, Institute of Natural Sciences and Mathematics, Ural Federal University, 19 Mira St., Yekaterinburg 620002, Russia

Mathematics, 2023, vol. 11, issue 16, 1-15

Abstract: In this paper, we define a differential operator on an open unit disk Δ by using the novel Borel distribution (BD) operator and means of convolution. This operator is adopted to introduce new subclasses of p -valent functions through the principle of differential subordination, and we focus on some interesting inclusion relations of these classes. Additionally, some inclusion relations are derived by using the Bernardi integral operator. Moreover, relevant convolution results are established for a class of analytic functions on Δ , and other results of analytic univalent functions are derived in detail. This study provides a new perspective for developing p -univalent functions with BD and offers valuable understanding for further research in complex analysis.

Keywords: p-valent function; Borel distribution; inclusion relation; integral operator; convolution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/16/3511/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/16/3511/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:16:p:3511-:d:1217068

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().